Solutions of elliptic equations involving critical Sobolev exponents with Neumann boundary conditions.
Myriam Comte, Mariette C. Knaap (1990)
Manuscripta mathematica
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Myriam Comte, Mariette C. Knaap (1990)
Manuscripta mathematica
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Carlos A. Berenstein, P.C. Yang (1987)
Journal für die reine und angewandte Mathematik
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Jan Chabrowski (2004)
Colloquium Mathematicae
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We consider the Neumann problem involving the critical Sobolev exponent and a nonhomogeneous boundary condition. We establish the existence of two solutions. We use the method of sub- and supersolutions, a local minimization and the mountain-pass principle.
J. Chabrowski, Jianfu Yang (2003)
Rendiconti del Seminario Matematico della Università di Padova
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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.
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.
P.J. McKenna, A.C. Lazer (1986)
Journal für die reine und angewandte Mathematik
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Jan Chabrowski (2011)
Colloquium Mathematicae
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We establish the existence of solutions for the Neumann problem for a system of two equations involving a homogeneous nonlinearity of a critical degree. The existence of a solution is obtained by a constrained minimization with the aid of P.-L. Lions' concentration-compactness principle.
Renate Schaaf (1984)
Journal für die reine und angewandte Mathematik
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Gabriella Tarantello (1993)
Manuscripta mathematica
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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.
Lawrence G. Brown (1994)
Journal für die reine und angewandte Mathematik
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Hanna Neumann (1963)
Journal für die reine und angewandte Mathematik
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N. Ghoussoub (1991)
Journal für die reine und angewandte Mathematik
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Olaf Neumann (1981)
Journal für die reine und angewandte Mathematik
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