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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_1007_s10587_012_0076_8,
     author = {Galewski, Marek and O'Regan, Donal},
     title = {Impulsive boundary value problems for $p(t)${-Laplacian's} via critical point theory},
     journal = {Czechoslovak Mathematical Journal},
     pages = {951--967},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {2012},
     doi = {10.1007/s10587-012-0076-8},
     mrnumber = {3010250},
     zbl = {1274.34083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0076-8/}
}
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
SP  - 951
EP  - 967
VL  - 62
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0076-8/
DO  - 10.1007/s10587-012-0076-8
LA  - en
ID  - 10_1007_s10587_012_0076_8
ER  - 
%0 Journal Article
%A Galewski, Marek
%A O'Regan, Donal
%T Impulsive boundary value problems for $p(t)$-Laplacian's via critical point theory
%J Czechoslovak Mathematical Journal
%D 2012
%P 951-967
%V 62
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0076-8/
%R 10.1007/s10587-012-0076-8
%G en
%F 10_1007_s10587_012_0076_8
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

Cité par Sources :