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Keywords:
$p( t)$-Laplacian; impulsive condition; critical point; variational method; Dirichlet problem
$p( t)$-Laplacian; impulsive condition; critical point; variational method; Dirichlet problem
Summary:
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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