Marek Galewski

The Existence of Solutions for a Semilinear Abstract Dirichlet Problem

We provide a new variational principle and duality for the problem
$$ Lu=\nabla G(u) , $$
where $L$ is selfadjoint and $\nabla G$ is a gradient mapping such that $G$ satisfies superquadratic growth conditions. The results obtained can be applied to Dirichlet problems for both ordinary and partial differential equations.

Dirichlet problem, existence, duality.

MSC 2000: 47J25, 47J30.