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1
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On multiple solutions of the Neumann problem involving the critical Sobolev exponent

100%
Chabrowski J.
Colloquium Mathematicum
|
2004
|
tom 101
|
nr 2
203-220
EN
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.
2
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On the Neumann problem for systems of elliptic equations involving homogeneous nonlinearities of a critical degree

100%
Chabrowski J.
Colloquium Mathematicum
|
2011
|
tom 125
|
nr 1
115-127
EN
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.
3
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On the critical Neumann problem with lower order perturbations

64%
Chabrowski J., Ruf B.
Colloquium Mathematicum
|
2007
|
tom 108
|
nr 2
225-246
EN
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.
4
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On the Neumann problem with combined nonlinearities

64%
Chabrowski J., Yang J.
Annales Polonici Mathematici
|
2005
|
tom 85
|
nr 3
239-250
EN
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.
5
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An Elliptic Neumann Problem with Subcritical Nonlinearity

64%
Chabrowski J., Tintarev K.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2005
|
tom 53
|
nr 1
7-16
EN
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.
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