| Title:
|
Impulsive boundary value problems for $p(t)$-Laplacian's via critical point theory (English) |
| Author:
|
Galewski, Marek |
| Author:
|
O'Regan, Donal |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
951-967 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
$p( t)$-Laplacian |
| Keyword:
|
impulsive condition |
| Keyword:
|
critical point |
| Keyword:
|
variational method |
| Keyword:
|
Dirichlet problem |
| MSC:
|
34B37 |
| MSC:
|
47J30 |
| MSC:
|
58E50 |
| idZBL:
|
Zbl 1274.34083 |
| idMR:
|
MR3010250 |
| DOI:
|
10.1007/s10587-012-0076-8 |
| . |
| Date available:
|
2012-11-10T21:34:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143038 |
| . |
| Reference:
|
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| Reference:
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