Displaying similar documents to “On the Neumann problem for systems of elliptic equations involving homogeneous nonlinearities of a critical degree”

On the critical Neumann problem with lower order perturbations

Jan Chabrowski, Bernhard Ruf (2007)

Colloquium Mathematicae

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We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent and lower order perturbations in bounded domains. Solutions are obtained by min max methods based on a topological linking. A nonlinear perturbation of a lower order is allowed to interfere with the spectrum of the operator -Δ with the Neumann boundary conditions.

On the Neumann problem for an elliptic system of equations involving the critical Sobolev exponent

J. Chabrowski, Jianfu Yang (2001)

Colloquium Mathematicae

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We consider the Neumann problem for an elliptic system of two equations involving the critical Sobolev nonlinearity. Our main objective is to study the effect of the coefficient of the critical Sobolev nonlinearity on the existence and nonexistence of least energy solutions. As a by-product we obtain a new weighted Sobolev inequality.

Remarks on positive solutions to a semilinear Neumann problem

Anna Maria Candela, Monica Lazzo (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper we study the influence of the domain topology on the multiplicity of solutions to a semilinear Neumann problem. In particular, we show that the number of positive solutions is stable under small perturbations of the domain.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

J. Chabrowski, E. Tonkes

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We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coefficients Q and h are at least continuous. Moreover Q is positive on Ω̅ and λ > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coefficients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by -Q....

On the Neumann problem with combined nonlinearities

Jan Chabrowski, Jianfu Yang (2005)

Annales Polonici Mathematici

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We establish the existence of multiple solutions of an asymptotically linear Neumann problem. These solutions are obtained via the mountain-pass principle and a local minimization.

Two constant sign solutions for a nonhomogeneous Neumann boundary value problem

Liliana Klimczak (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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We consider a nonlinear Neumann problem with a nonhomogeneous elliptic differential operator. With some natural conditions for its structure and some general assumptions on the growth of the reaction term we prove that the problem has two nontrivial solutions of constant sign. In the proof we use variational methods with truncation and minimization techniques.

An Elliptic Neumann Problem with Subcritical Nonlinearity

Jan Chabrowski, Kyril Tintarev (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.