Unbounded solutions for functional problems on the half-line

This paper presents an existence and localization result of unbounded solutions for a second-order differential equation on the half-line with functional boundary conditions. By applying unbounded upper and lower solutions, Green's functions and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an Emden-Fowler equation are shown to illustrate our results.

Unbounded solutions for functional problems on the half-line

This paper presents an existence and localization result of unbounded solutions for a second-order differential equation on the half-line with functional boundary conditions. By applying unbounded upper and lower solutions, Green's functions and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an Emden-Fowler equation are shown to illustrate our results.

Solvabilty of generalized Hammerstein integral equations on unbounded domains, with sign-changing kernels

In this work we study an Hammerstein generalized integral equation u(t)=∫_{-∞}^{+∞}k(t,s) f(s,u(s),u′(s),...,u^{(m)}(s))ds, where k:ℝ²→ℝ is a W^{m,∞}(ℝ²), m∈ℕ, kernel function and f:ℝ^{m+2}→ℝ is a L¹-Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Avaliação da performance organizacional e gestão estratégica no sector público; contributos para a construção de um balanced scorecard na Universidade de Évora: Trabalho de projecto

A Administração Pública tem sido alvo de uma reflexão sistemática, que pretende encontrar políticas de gestão que consigam solucionar os problemas de performance dos serviços públicos, evidenciando as suas potencialidades e procurando responder aos desafios com que se confrontam na atualidade. O fenómeno da globalização está na origem de acelerados ciclos de mudança que exigem das organizações urna gestão mais cativa e objetiva, alicerçada em métodos de gestão moderna que vão de encontro às exigências do mundo atual. Eficiência e eficácia dos serviços públicos são, mais do que nunca, duas imposições de uma sociedade crítica e carente de qualidade. A melhoria da performance do serviço público, mais do que urna necessidade, é uma exigência. Como responder a este desafio? Regra geral, os serviços públicos possuem urna fraca cultura de gestão estratégica, o que justifica parte da dificuldade que sentem em transformar a estratégia em objetivos operacionais, de forma a estabelecer ações que visem a obtenção de resultados, definindo medidas para a sua monitorização. O Balanced Scorecard (BSC) poderá contribuir para a implementação de uma cultura de gestão estratégica no Sector Público. A formulação dos objetivos estratégicos, das metas e dos indicadores, para cada uma das perspetivas subjacentes a esta metodologia, permite às organizações efetuarem uma gestão mais adequada dos sistemas que são objeto da sua acão. Este trabalho, partindo da identificação dos ajustamentos que é necessário efetuar ao modelo original de BSC de Kaplan e Norton, propõe um BSC adequado às Instituições de Ensino Superior Público (IESP) em geral e à Universidade de Évora em particular, assumindo-se que esse BSC poderá constituir uma importante ferramenta de gestão estratégica, essencial na avaliação e gestão da performance organizacional. ABSTRACT: The Public Administration has been the target of a systematic reflexion, who wish to find management policies that can resolve the performance problems on public services, showing their potential and aim to respond to the challenges they are facing today. The phenomenon of globalization is the cause of accelerated cycles of change that require organizations a more active and objective management, based on modern management methods that meet the demands of today’s world. Efficiency and effectiveness of public services are more than ever, two charges of a society criticism and lacking in quality. Improving the performance of public service, rather than a necessity is a requirement. How to respond to this challenge? Generally, the public services have a weak culture of strategic management, which explains part of the difficulty they feel in turning the strategy into operational objectives in order to establish measures aimed at achieving results, defining measures for its monitoring. The Balanced Scorecard can contribute to the implementation of a culture of strategic management in the Public Sector. The formulation of strategic objectives, targets and indicators for each of the perspectives that underlie this methodology enables organizations to make better management systems that are the subject of its action. This work, leaving from the identification of the adjustments that is necessary to effectuate to an original model of BSC of Kaplan and Norton, proposes a BSC appropriate to the Institutions of Superior Public Teaching (IESP) in general and to the University of Évora in individual, when are assumed that this BSC will be able to constitute an important tool of strategic, essential management in the evaluation and management of the organizational performance.

Sufficient conditions for the existence of heteroclinic solutions for Phi-Laplacian differential equations

In this paper we consider the second order discontinuous equation in the real line, (a(t)φ(u′(t)))′ = f(t,u(t),u′(t)), a.e.t∈R, u(-∞) = ν⁻, u(+∞)=ν⁺, with φ an increasing homeomorphism such that φ(0)=0 and φ(R)=R, a∈C(R,R\{0})∩C¹(R,R) with a(t)>0, or a(t)<0, for t∈R, f:R³→R a L¹-Carathéodory function and ν⁻,ν⁺∈R such that ν⁻<ν⁺. We point out that the existence of heteroclinic solutions is obtained without asymptotic or growth assumptions on the nonlinearities φ and f. Moreover, as far as we know, this result is even new when φ(y)=y, that is, for equation (a(t)u′(t))′=f(t,u(t),u′(t)), a.e.t∈R.