Czechoslovak Mathematical Journal

, Volume 62, Issue 4, pp 951–967

Impulsive boundary value problems for p(t)-Laplacian’s via critical point theory


DOI: 10.1007/s10587-012-0076-8

Cite this article as:
Galewski, M. & O’Regan, D. Czech Math J (2012) 62: 951. doi:10.1007/s10587-012-0076-8


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.


p(t)-Laplacian impulsive condition critical point variational method Dirichlet problem 

MSC 2010

34B37 47J30 

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2012

Authors and Affiliations

  1. 1.Institute of MathematicsTechnical University of LodzLodzPoland
  2. 2.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland

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