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1
Content available On a singular nonlinear Neumann problem
Chabrowski J.
Opuscula Mathematica
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2014
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Vol. 34, no. 2
271--290
EN
We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: (i) 2 < p+1 <2*s, (ii) p+1 = 2*(s) and (iii) 2*(s) < p+1 ≤ 2*, where [formula] denote the critical Hardy-Sobolev exponent and the critical Sobolev exponent, respectively.
2
Content available The Hardy potential and eigenvalue problems
Chabrowski J.
Opuscula Mathematica
|
2011
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Vol. 31, no. 2
173-194
EN
We establish the existence of principal eigenfunctions for the Laplace operator involving weighted Hardy potentials. We consider the Dirichlet and Neumann boundary conditions.
3
Content available On elliptic problems with a nonlinearity depending on the gradient
Chabrowski J.
Opuscula Mathematica
|
2009
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Vol. 29, no. 4
377-391
EN
We investigate the solvability of the Neumann problem (1.1) involving the non-linearity depending on the gradient. We prove the existence of a solution when the right hand side ƒ of the equation belongs to Lm( Ω) with 1 ≤m <2.
4
Content available remote Indefinite quasilinear Neumann problem on unbounded domains
Chabrowski J.
Bulletin of the Polish Academy of Sciences. Mathematics
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2006
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Vol. 54, no 3-4
207-217
EN
We investigate the solvability of the quasilinear Neumann problem (1.1) with sub- and supercritical exponents in an unbounded domain Ω. Under some integrability conditions on the coefficients we establish embedding theorems of weighted Sobolev spaces into weighted Lebesgue spaces. This is used to obtain solutions through a global minimization of a variational functional.
5
Content available remote An elliptic Neumann problem with subcritical nonlinearity
Chabrowski J., Tintarev K.
Bulletin of the Polish Academy of Sciences. Mathematics
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2005
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Vol. 53, no 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.
6
Content available remote On the nonlinear Neumann problem with indefinite weight and Sobolev critical nonlinearity
Chabrowski J.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2002
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Vol. 50, no 3
323-333
EN
We prove the existence of positive solutions of the Neumann problem with indefinite weight and critical Sobolev nonlinearity. Our approach is based on the concentration-compactness principle applied to a related variational problem.
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