Browsing by Author "Chabrowski, Jan"

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Access status: Open Access ,
On a singular nonlinear Neumann problem
(2014) Chabrowski, Jan
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: $\text{(i)}\;\ 2\lt p+1\lt 2^*(s),$, $\text{(ii)}\;\ p+1=2^*(s)$ and $\text{(iii)}\;\ 2^*(s)\lt p+1 \leq 2^*,$ where $2^*(s)=\frac{2(N-s)}{N-2},$ $0\lt s\lt 2,$ and $2^*=\frac{2N}{N-2}$ denote the critical Hardy-Sobolev exponent and the critical Sobolev exponent, respectively.
Access status: Open Access ,
On elliptic problems with a nonlinearity depending on the gradient
(2009) Chabrowski, Jan
We investigate the solvability of the Neumann problem $(1.1)$ involving the nonlinearity depending on the gradient. We prove the existence of a solution when the right hand side $f$ of the equation belongs to $L^m(\Omega )$ with $1 \leq m \lt 2$.
Access status: Open Access ,
The Hardy potential and eigenvalue problems
(2011) Chabrowski, Jan
We establish the existence of principal eigenfunctions for the Laplace operator involving weighted Hardy potentials. We consider the Dirichlet and Neumann boundary conditions.