Abstract
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.
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Galewski, M., O’Regan, D. Impulsive boundary value problems for p(t)-Laplacian’s via critical point theory. Czech Math J 62, 951–967 (2012). https://doi.org/10.1007/s10587-012-0076-8
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DOI: https://doi.org/10.1007/s10587-012-0076-8