Impulsive boundary value problems for p(t)-Laplacian’s via critical point theory
- First Online:
- Cite this article as:
- Galewski, M. & O’Regan, D. Czech Math J (2012) 62: 951. doi:10.1007/s10587-012-0076-8
- 160 Downloads
In this paper we investigate the existence of solutions to impulsive problems with a p(t)-Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence of at least one weak solution to the nonlinear problem.