Impulsive boundary value problems for $p(t)$-Laplacian's via critical point theory
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 951-967.

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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.
DOI : 10.1007/s10587-012-0076-8
Classification : 34B37, 47J30, 58E50
Mots-clés : $p( t)$-Laplacian; impulsive condition; critical point; variational method; Dirichlet problem 
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     title = {Impulsive boundary value problems for $p(t)${-Laplacian's} via critical point theory},
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Galewski, Marek; O'Regan, Donal. Impulsive boundary value problems for $p(t)$-Laplacian's via critical point theory. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 951-967. doi : 10.1007/s10587-012-0076-8. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0076-8/

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