On the nonlinear Neumann problem involving the critical Sobolev exponent on the boundary

in this paper we investigate the solvability of the Neumann problem (1.1) involving the critical Sobolev exponents on the right-hand side of the equation and in the boundary condition. It is assumed that the coefficients Q and P are smooth. We examine the common effect of the mean curvature of the boundary a deltaOhm and the shape of the graph of the coefficients Q and P on the existence of solutions of problem (1.1). (C) 2003 Published by Elsevier Inc.

On the Schrodinger equation involving a critical Sobolev exponent and magnetic field

We consider the semilinear Schrodinger equation -Delta(A)u + V(x)u = Q(x)vertical bar u vertical bar(2* -2) u. Assuming that V changes sign, we establish the existence of a solution u not equal 0 in the Sobolev space H-A,V(1) + (R-N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Delta(A).

Sharp Sobolev inequality involving a critical nonlinearity on a boundary

We consider the solvability of the Neumann problem for the equation -Delta u + lambda u = 0, partial derivative u/partial derivative v = Q(x)vertical bar u vertical bar(q-2)u on partial derivative Omega, where Q is a positive and continuous coefficient on partial derivative Omega, lambda is a parameter and q = 2(N - 1)/(N - 2) is a critical Sobolev exponent for the trace embedding of H-1(Omega) into L-q(partial derivative Omega). We investigate the joint effect of the mean curvature of partial derivative Omega and the shape of the graph of Q on the existence of solutions. As a by product we establish a sharp Sobolev inequality for the trace embedding. In Section 6 we establish the existence of solutions when a parameter lambda interferes with the spectrum of -Delta with the Neumann boundary conditions. We apply a min-max principle based on the topological linking.

On multiple solutions of the exterior neumann problem involving critical sobolev exponent

In this paper we consider the exterior Neumann problem involving a critical Sobolev exponent. We establish the existence of two solutions having a prescribed limit at infinity.

Existence of solutions for p(x)-Laplacian problems on a bounded domain

In this paper we study the following p(x)-Laplacian problem: -div(a(x)&VERBAR;&DEL; u&VERBAR;(p(x)-2)&DEL; u)+b(x)&VERBAR; u&VERBAR;(p(x)-2)u = f(x, u), x ε &UOmega;, u = 0, on &PARTIAL; &UOmega;, where 1< p(1) &LE; p(x) &LE; p(2) < n, &UOmega; &SUB; R-n is a bounded domain and applying the mountain pass theorem we obtain the existence of solutions in W-0(1,p(x)) for the p(x)-Laplacian problems in the superlinear and sublinear cases. © 2004 Elsevier Inc. All rights reserved.

Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.

Relationships between quality of experience and participation in diverse performance settingshttp://espace.library.uq.edu.au/workflow/edit_metadata.php?id=382160&wfs_id=778

The flow concept describes a model of enjoyment that has relevance for understanding participation and experience across a wide range of activities (Csikszentmihalyi, 1997). The basic premise of the flow concept is that when challenges and skills are simultaneously balanced and extending the individual, a state of total absorption can occur. Research by Jackson and colleagues has examined the utility of the flow concept to understanding participation and performance in sport settings. Recently, Jackson and Eklund have examined flow in a range of performance settings: sport, exercise, dance, creative and performing arts, and music. In this paper, we present descriptive and construct validity data on how participants in these activities experienced flow, as assessed by the recently revised flow scales: The Dispositional Flow Scale-2 (DFS-2) and Flow State Scale-2 (FSS-2) (Jackson & Eklund, 2002). The fmdings will be discussed in relation to the utility of the flow concept to understanding participation across performance settings.

Reactions catalyzed by bacterial cytochromes P450

The cytochromes P450 are a large family of oxidative haemoproteins that are responsible for a wide variety of oxidative transformations in a variety of organisms. This review focuses upon the reactions catalyzed specifically by bacterial enzymes, which includes aliphatic hydroxylation, alkene epoxidation, aromatic hydroxylation, oxidative phenolic coupling, heteroatom oxidation and dealkylation, and multiple oxidations including C-C bond cleavage. The potential for the practical application of the oxidizing power of these enzymes is briefly discussed.

Products of Cytochrome P450BioI (CYP107H1)-Catalyzed Oxidation of Fatty Acids

[GRAPHICS] Oxidation of tetradecanoic and hexadecanoic acids by cytochrome P450(Biol) (CYP107H1) produces mainly the 11-, 12-, and 13-hydroxy C-14 fatty acids and the 11- to 15-hydroxy C-16 fatty acids, respectively. In contrast to previous reports, terminal hydroxylation is not observed. The enantiospecificity of fatty acid hydroxylation by P450(Biol) was also determined, and the enzyme was shown to be moderately selective for production of the (R)-alcohols.

Thermal characterization of polyester-melamine coating matrices prepared under nonisothermal conditions

Thermal analysis methods (differential scanning calorimetry, thermogravimetric analysis, and dynamic mechanical thermal analysis) were used to characterize the nature of polyester-melamine coating matrices prepared under nonisothermal, high-temperature, rapid-cure conditions. The results were interpreted in terms of the formation of two interpenetrating networks with different glass-transition temperatures (a cocondensed polyester-melamine network and a self-condensed melamine-melamine network), a phenomenon not generally seen in chemically similar, isothermally cured matrices. The self-condensed network manifested at high melamine levels, but the relative concentrations of the two networks were critically dependent on the cure conditions. The optimal cure (defined in terms of the attainment of a peak metal temperature) was achieved at different oven temperatures and different oven dwell times, and so the actual energy absorbed varied over a wide range. Careful control of the energy absorption, by the selection of appropriate cure conditions, controlled the relative concentrations of the two networks and, therefore, the flexibility and hardness of the resultant coatings. (C) 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Cbem 41: 1603-1621, 2003.