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

Galewski, Marek
; 
O’Regan, Donal
Identifiers
http://hdl.handle.net/10379/11573
https://doi.org/10.13025/27020
Repository DOI
10.1007/s10587-012-0076-8
Publication Date
2012-12-01
Keywords
p(t)-laplacian, impulsive condition, critical point, variational method, dirichlet problem, differential-equations, positive solutions, growth
Type
Article
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Citation
Galewski, Marek; O’Regan, Donal (2012). Impulsive boundary value problems for p(t)-laplacian’s via critical point theory. Czechoslovak Mathematical Journal 62 (4), 951-967
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.
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Publisher
Institute of Mathematics, Czech Academy of Sciences
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)