Browsing by Subject "Neumann problem"

Now showing 1 - 3 of 3

Access status: Open Access ,
Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian
(2014) Candito, Pasquale; D’Aguí, Giuseppina
In this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete $p$-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.
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 $1 \leq m \lt 2$.