Positive Solution for a Class of Degenerate Quasilinear Elliptic Equations in R-N

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Oscillation Properties of Some Functional Fourth Order Ordinary Differential Equations

2010 Mathematics Subject Classification: 34A30, 34A40, 34C10.

On the Zeros of the Solutions to Nonlinear Hyperbolic Equations with Delays

2002 Mathematics Subject Classification: Primary 35В05; Secondary 35L15

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Global behavior of positive solutions of nonlinear three-point boundary value problems

We investigate the structure of the positive solution set for nonlinear three-point boundary value problems of the form u('') + h(t) f(u) = 0, u(0) = 0, u(1) = lambdau(eta), where eta epsilon (0, 1) is given lambda epsilon (0, 1/n) is a parameter, f epsilon C ([0, infinity), [0, infinity)) satisfies f (s) > 0 for s > 0, and h epsilon C([0, 1], [0, infinity)) is not identically zero on any subinterval of [0, 1]. Our main results demonstrate the existence of continua of positive solutions of the above problem. (C) 2004 Elsevier Ltd. All rights reserved.

Positive solutions for parametric Dirichlet problems with indefinite potential and superdiffusive reaction

We consider a parametric semilinear Dirichlet problem driven by the Laplacian plus an indefinite unbounded potential and with a reaction of superdifissive type. Using variational and truncation techniques, we show that there exists a critical parameter value λ_{∗}>0 such that for all λ> λ_{∗} the problem has least two positive solutions, for λ= λ_{∗} the problem has at least one positive solutions, and no positive solutions exist when λ∈(0,λ_{∗}). Also, we show that for λ≥ λ_{∗} the problem has a smallest positive solution.

电离层胶片频高图数字化转换与分析研究

The ionogram acquired with the ionospheric vertical sounding method is the oldest data in the history of ionospheric research. Using of modern microelectronics and computer technology to digitalize, analyse and preserve the huge amount of historical film ionogram has become more and more important and urgent. This paper introduced the progress of the film ionogram digitalization by using digital image processing technologies to correct and repair film ionogram and convert them in an exchangeable format. An analysis and conversion software, basing on this method, has been developed for the film ionogram analysis, and then it introduces the application of this software by combining the SAO Explorer program for Wuhan film ionogram and pseudo-color ionogram in Yamagawa in Japan. It shows that our method is reliable，and the developed software is used friendly and provides a positive solution in digitalization and analysis of huge amount of historical film ionogram. Firstly, we briefly introduce the film ionogram and the process of its digitalization. By observing a amount of film ionogram, we obtain some common characteristics of the digitalized film ionogram following as: (1) the image rotation are caused by scanning; (2) the vertical axis of a large number of film ionogram exist more or less tilt and bending ; (3) coordinates of the film ionogram appear the non-uniformity phenomena result from the instability of driving motor rotation and the error of altitudinal cursor orientation. Moreover, based on the characteristics of the film ionogram and the SAO Explorer software which is widely used for the digital ionogram analysis in the world, a new method has been developed for film ionogram procession. The method contains the image geometric correction and film ionogram format conversion. The image geometric correction includes such as image rotation correction, vertical correction and coordinates scale correction. After geometric correction, the BMP file format images will be converted to the SBF file format images. Then, we also discuss the data format converting methods, which include two methods of the image data mapping basing on the normalization and logarithm, and the method of the preprocessing of the noise filtering and the threshold setting. Combining with SAO Explorer software, we successfully obtain ionospheric parameters and electron profile from the converted SBF file format digital ionograms. Based on the above method, we developed the software for the film ionogram to realize its correction analysis and conversion of the image format, and then give a introduction for its function and operation. Subsequently, the software are applied into the Wuhan film ionogram which separately observed in the high solar activity year and the low in 1980s last century. The results reveal the converted SBF digital ionogram almost preserve the all echo information of the film ionogram. Furthermore, we expressly discuss the application to the Wuhan film ionogram in 1958 in order to validate the applicability and credibility of the software. And it is showed that the important information of the film ionogram are maintained into the SBF digital ionogram. It is represented that there is credibility for conversion of the software when it applied in the older film ionogram. In sum, this software could apply to the digitalization and analysis of huge amount of historical film ionogram. Last, we extended the function of the software by bring some new conversion method and used it to apply to the pseudo-color ionogram of yamagawa in Japan. The results show that the converted ionogram information basically maintain the importantly ionogram information and the error of scaling of converted SBF file format image is almost acceptable, though there is no preprocessing for the original ionogram. Hence, we could extend the applicable range of the software and apply it to all kinds of simulative ionogram imaging by improving the method and software.

Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

Problemas elípticos com potencial que pode tender a zero no in?nito

Pós-graduação em Matemática - IBILCE

Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GROUND STATE AND NON-GROUND STATE SOLUTIONS OF SOME STRONGLY COUPLED ELLIPTIC SYSTEMS

We study an elliptic system of the form Lu = vertical bar v vertical bar(p-1) v and Lv = vertical bar u vertical bar(q-1) u in Omega with homogeneous Dirichlet boundary condition, where Lu := -Delta u in the case of a bounded domain and Lu := -Delta u + u in the cases of an exterior domain or the whole space R-N. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.

Tolerance and Critical Thinking

Post-soviet countries are in the process of transformation from a totalitarian order to a democratic one, a transformation which is impossible without a profound shift in people's way of thinking. The group set themselves the task of determining the essence of this shift. Using a multidisciplinary approach, they looked at concrete ways of overcoming the totalitarian mentality and forming that necessary for an open democratic society. They studied the contemporary conceptions of tolerance and critical thinking and looked for new foundations of criticism, especially in hermeneutics. They then sought to substantiate the complementary relation between tolerance and criticism in the democratic way of thinking and to prepare a a syllabus for teaching on the subject in Ukrainian higher education. In a philosophical exploration of tolerance they began with relgious tolerance as its first and most important form. Political and social interests often lay at the foundations of religious intolerance and this implicitly comprised the transition to religious tolerance when conditions changed. Early polytheism was more or less indifferent to dogmatic deviations but monotheism is intolerant of heresies. The damage wrought by the religious wars of the Reformations transformed tolerance into a value. They did not create religious tolerance but forced its recognition as a positive phenomenon. With the weakening of religious institutions in the modern era, the purely political nature of many conflicts became evident and this stimulated the extrapolation of tolerance into secular life. Each historical era has certain acts and operations which may be interpreted as tolerant and these can be classified as to whether or not they are based on the conscious following of the principle of tolerance. This criterion requires the separation of the phenomenon of tolerance from its concept and from tolerance as a value. Only the conjunction of a concept of tolerance with a recognition of its value can transform it into a principle dictating a norm of conscious behaviour. The analysis of the contemporary conception of tolerance focused on the diversity of the concept and concluded that the notions used cannot be combined in the framework of a single more or less simple classification, as the distinctions between them are stimulated by the complexity of the realty considered and the variety of its manifestations. Notions considered in relation to tolerance included pluralism, respect and particular-universal. The rationale of tolerance was also investigated and the group felt that any substantiation of the principle of tolerance must take into account human beings' desire for knowledge. Before respecting or being tolerant of another person different from myself, I should first know where the difference lies, so knowledge is a necessary condition of tolerance.The traditional division of truth into scientific (objective and unique) and religious, moral, political (subjective and so multiple) intensifies the problem of the relationship between truth and tolerance. Science was long seen as a field of "natural" intolerance whereas the validity of tolerance was accepted in other intellectual fields. As tolerance eemrges when there is difference and opposition, it is essentially linked with rivaly and there is a a growing recognition today that unlimited rivalry is neither able to direct the process of development nor to act as creative matter. Social and economic reality has led to rivalry being regulated by the state and a natural requirement of this is to associate tolerance with a special "purified" form of rivalry, an acceptance of the actiivity of different subjects and a specification of the norms of their competition. Tolerance and rivalry should therefore be subordinate to a degree of discipline and the group point out that discipline, including self-discipline, is a regulator of the balance between them. Two problematic aspects of tolerance were identified: why something traditionally supposed to have no positive content has become a human activity today, and whether tolerance has full-scale cultural significance. The resolution of these questions requires a revision of the phenomenon and conception of tolerance to clarify its immanent positive content. This involved an investigation of the contemporary concept of tolerance and of the epistemological foundations of a negative solution of tolerance in Greek thought. An original soution to the problem of the extrapolation of tolerance to scientific knowledge was proposed based on the Duhem-Quine theses and conceptiion of background knowledge. In this way tolerance as a principle of mutual relations between different scientific positions gains an essential epistemological rationale and so an important argument for its own universal status. The group then went on to consider the ontological foundations for a positive solution of this problem, beginning with the work of Poincare and Reichenbach. The next aspect considered was the conceptual foundations of critical thinking, looking at the ideas of Karl Popper and St. Augustine and at the problem of the demarcation line between reasonable criticism and apologetic reasoning. Dogmatic and critical thinking in a political context were also considered, before an investigation of critical thinking's foundations. As logic is essential to critical thinking, the state of this discipline in Ukrainian and Russian higher education was assessed, together with the limits of formal-logical grounds for criticism, the role of informal logical as a basis for critical thinking today, dialectical logic as a foundation for critical thinking and the universality of the contemporary demand for criticism. The search for new foundations of critical thinking covered deconstructivism and critical hermeneutics, including the problem of the author. The relationship between tolerance and criticism was traced from the ancient world, both eastern and Greek, through the transitional community of the Renaissance to the industrial community (Locke and Mill) and the evolution of this relationship today when these are viewed not as moral virtues but as ordinary norms. Tolerance and criticism were discussed as complementary manifestations of human freedom. If the completeness of freedom were accepted it would be impossible to avoid recognition of the natural and legal nature of these manifestations and the group argue that critical tolerance is able to avoid dismissing such negative phenomena as the degradation of taste and manner, pornography, etc. On the basis of their work, the group drew up the syllabus of a course in "Logic with Elements of Critical Thinking, and of a special course on the "Problem of Tolerance".

Seals and the Need for more Deference to Vienna by WTO Adjudicators

This paper asks how World Trade Organization (WTO) panels and the Appellate Body (AB) take public international law (PIL) into account when interpreting WTO rules as a part of international economic law (IEL). Splendid isolation of the latter is not new; indeed it is intended by the negotiators of the Understanding on the Settlement of Disputes (DSU). At the same time, the Vienna Convention on the Law of Treaties (VCLT) is quite clear when it provides the general rules and the supplementary means of treaty interpretation. Despite such mandatory guidance, WTO adjudicators (when given a choice and assuming they see the conflict) prefer deference to WTO law over deference to Vienna and take a dogmatic way out of interpretation quandaries. The AB and panels make abundant reference to Vienna, though less so to substantive PIL. Often times, however, they do so simply in order to buttress their findings of violations of WTO rules. Perhaps tellingly, however, none of the reports in EC – Seals contains even a single mention of VCLT, despite numerous references to international standards addressing indigenous rights and animal welfare. In the longer term, and absent a breakthrough on the negotiation front, this pattern of carefully eschewing international treaty law and using PIL just for the sake of convenience could have serious consequences for the credibility and acceptance of the multilateral trading system. Following the adage ‘negotiate or litigate’ recourse to WTO dispute settlement increases when governments are less ready to make treaty commitments commensurate with the challenges of globalisation. This is true even for ‘societal choice’ cases on the margins of classic trade disputes. We will argue here that it is precisely for cases such as these that VCLT and PIL should be used more systematically by panels and the AB. Failing that, instead of building bridges for more coherent international regulation, WTO adjudicators could burn those same bridges which the DSU interpretation margin leaves open for accomplishing their job which is to find a ‘positive solution’. Worse, judicial incoherence could return to WTO dispute settlement like a boomerang and damage the credibility and thus the level of acceptance of the multilateral trading system per se.

ロシアの中東政策 -- プーチン大統領のシリア政策を通じて

The active initiative taken by Russian President Vladamir Putin by bombarding the antigovernment forces in Syria at the end of September 2015 startled the world by its precalculated boldness. Russian intervention has radically changed the dynamic of the war by empowering the Syrian government of Bashar Assad, and has resulted in a ceasefire agreement which starts on 27th February 2016, led by Russia and the US. No one can predict at present the next stage of conflicts in Syria or whether it will result in a positive solution to the tragic wars there. However, there is no denying the fact that Russia has played an important role in the development of the game. This paper analyzes the motivations of Putin in intervening in the Syrian crisis and the factors which have enabled Russia to play an enlarged role in the Middle East, seemingly beyond its objective capabilities. Legacies of international networks built during the Soviet period; shrewd tactics in making use of the inconsistency and vacillation of US policies, particularly towards the Middle East; its historical experience of interaction with the Muslim cultures, including domestic ones; its geopolitical perception of world politics, and the export of energy resources and military weapons as tools of diplomacy are some of the factors which explain Russian behavior. At the same time, the personal leadership and accumulated experience of President Putin in formulating Russian diplomacy and in manipulating different issues in a combined policy should be taken into account. His initiative in Syria succeeded to some extent in turning world attention away from the Ukrainian issue, aimed at changing the present sanctions imposed by the West. Another phenomenon to be noted in the international arena is the newly developed mutual interaction between Russia and the Arab countries in the Gulf. Frequent visits to Russia by autocratic leaders, including kings, emirsand princes do not always reflect a shared common interest between Russia and the Arab leaders. On the contrary, in spite of sharp and fundamental differences in their attitude toward the issues related to Syria, Iran and Yemen, the Arab leaders find it necessary to communicate with Russia and to know Russia’s expected strategies and intentions towards the Middle East, apart from its oil and gas policies. The Iran deal on the nuclear issue in July 2015 may have been a factor behind the phenomena.

Nonlinear, nonhomogeneous parametric Neumann problems

We consider a parametric nonlinear Neumann problem driven by a nonlinear nonhomogeneous differential operator and with a Caratheodory reaction $f\left( t,x\right) $ which is $p-$superlinear in $x$ without satisfying the usual in such cases Ambrosetti-Rabinowitz condition. We prove a bifurcation type result describing the dependence of the positive solutions on the parameter $\lambda>0,$ we show the existence of a smallest positive solution $\overline{u}_{\lambda}$ and investigate the properties of the map $\lambda\rightarrow\overline{u}_{\lambda}.$ Finally we also show the existence of nodal solutions.