Geodesic
Impulsive boundary value problems for $p(t)$-Laplacian's via critical point theory
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 4, pp. 951-967 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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

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