The paper presents existence and multiplicity results for non-linear boundary value problems on possibly non-smooth and unbounded domains under possibly non-homogeneous Dirichlet boundary conditions. We develop here an appropriate functional setting based on weighted Sobolev spaces. Our results are obtained by using global minimization and a minimax approach using a non-smooth critical point theory.
- global optimization
- minimax principle
- non-homogeneous Dirichlet boundary conditions
- non-linear elliptic problem
- weighted Sobolev spaces