**
Czechoslovak Mathematical Journal, Vol. 62, No. 4, pp. 951-967, 2012
**

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

##
Marek Galewski, Donal O'Regan

* Marek Galewski*, Institute of Mathematics, Technical University of Łódź, Wolczanska 215, 90-924 Łódź, Poland, e-mail: ` marek.galewski@p.lodz.pl`; * Donal O'Regan*, School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland, e-mail: ` donal.oregan@nuigalway.ie`

**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.

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

**Classification (MSC 2010):** 34B37, 47J30

**Full text** available as PDF.

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade.
To activate your access, please contact Myris Trade at myris@myris.cz.

Subscribers of Springer need to access the articles on their site, which is http://www.springeronline.com/10587.