Impulsive boundary value problems for -Laplacian’s via critical point theory
Czechoslovak Mathematical Journal (2012)
- Volume: 62, Issue: 4, page 951-967
- ISSN: 0011-4642
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topGalewski, Marek, and O'Regan, Donal. "Impulsive boundary value problems for $p(t)$-Laplacian’s via critical point theory." Czechoslovak Mathematical Journal 62.4 (2012): 951-967. <http://eudml.org/doc/246575>.
@article{Galewski2012,
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.},
author = {Galewski, Marek, O'Regan, Donal},
journal = {Czechoslovak Mathematical Journal},
keywords = {$p( t)$-Laplacian; impulsive condition; critical point; variational method; Dirichlet problem; -Laplacian; impulsive condition; critical point; variational method; Dirichlet problem},
language = {eng},
number = {4},
pages = {951-967},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Impulsive boundary value problems for $p(t)$-Laplacian’s via critical point theory},
url = {http://eudml.org/doc/246575},
volume = {62},
year = {2012},
}
TY - JOUR
AU - Galewski, Marek
AU - O'Regan, Donal
TI - Impulsive boundary value problems for $p(t)$-Laplacian’s via critical point theory
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 951
EP - 967
AB - 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.
LA - eng
KW - $p( t)$-Laplacian; impulsive condition; critical point; variational method; Dirichlet problem; -Laplacian; impulsive condition; critical point; variational method; Dirichlet problem
UR - http://eudml.org/doc/246575
ER -
References
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