Multiplicity results for an inhomogeneous Neumann problem with critical exponent.
Gabriella Tarantello (1993)
Manuscripta mathematica
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Displaying similar documents to “Solutions of elliptic equations involving critical Sobolev exponents with Neumann boundary conditions.”
Multiplicity results for an inhomogeneous Neumann problem with critical exponent.
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 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.
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.
A nonexistence theorem for an equation with critical Sobolev exponent in the half space.
H. Berestycki, M. Gross, F. Pacella (1992)
Manuscripta mathematica
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Multiplicity of positive solutions of nonlinear elliptic equations with critical sobolev exponent in some contractible domains.
Donato Passaseo (1989)
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.
A Note on the Problem -...u = ...u + u| u|2*-2.
M. Struwe, A. Ambrosetti (1986)
Manuscripta mathematica
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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 positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities
J. Chabrowski, P. Drábek (2002)
Studia Mathematica
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We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.
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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Geometry and topology of the boundary in the critical Neumann problem.
G. Mancini, Adimurthi (1994)
Journal für die reine und angewandte Mathematik
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On elliptic systems pertaining to the Schrödinger equation
J. Chabrowski, E. Tonkes (2003)
Annales Polonici Mathematici
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We discuss the existence of solutions for a system of elliptic equations involving a coupling nonlinearity containing a critical and subcritical Sobolev exponent. We establish the existence of ground state solutions. The concentration of solutions is also established as a parameter λ becomes large.
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.
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.