Existence results for some nonlinear and noncoercive anisotropic elliptic equations with Neumann boundary conditions
Abstract
The aim of this work is to prove the existence of renormalized solutions for the following anisotropic elliptic problem with degenerate coercivity and Fourier boundary conditions
- \sum_{i=1}^{N}D^i a_i(x,u,\nabla u) + g(x,u,\nabla u) + \alpha(x)|u|^{r-1}u = f in \Omega,
\sum_{i=1}^{N}a_i(x,u,\nabla u).n_i+\lambda u = 0 on \partial\Omega,
where \Omega is an open bounded subset of IR^N (N\geq 2), and the data f belong to L^{1}(\Omega) and the Carathéodory functions a_{i}(x,s,\xi) and g(x,s,\xi) verify some nonstandard conditions.
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