The role of the boundary in some semilinear Neumann problems
Giovanni Mancini, Roberta Musina (1992)
Rendiconti del Seminario Matematico della Università di Padova
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Displaying similar documents to “Remarks on positive solutions to a semilinear Neumann problem”
The role of the boundary in some semilinear Neumann problems
Multiple solutions of a nonlinear elliptic equation involving Neumann conditions and a critical Sobolev exponent
J. Chabrowski, Jianfu Yang (2003)
Rendiconti del Seminario Matematico della Università di Padova
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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.
Non existence of bounded-energy solutions for some semilinear elliptic equations with a large parameter
Daniele Castorina, Gianni Mancini (2003)
Rendiconti del Seminario Matematico della Università di Padova
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On multiple solutions of the Neumann problem involving the critical Sobolev exponent
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.
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.
Solutions of elliptic equations involving critical Sobolev exponents with Neumann boundary conditions.
Myriam Comte, Mariette C. Knaap (1990)
Manuscripta mathematica
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On the Neumann problem for systems of elliptic equations involving homogeneous nonlinearities of a critical degree
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.
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.
Mean curvature and least energy solutions for the critical Neumann problem with weight
J. Chabrowski (2002)
Bollettino dell'Unione Matematica Italiana
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In this paper we consider the Neumann problem involving a critical Sobolev exponent. We investigate a combined effect of the coefficient of the critical Sobolev nonlinearity and the mean curvature on the existence and nonexistence of solutions.
On the Neumann problem with L¹ data
J. Chabrowski (2007)
Colloquium Mathematicae
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We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.
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.