| Title:
|
Periodic solutions for some nonautonomous $p(t)$-Laplacian Hamiltonian systems (English) |
| Author:
|
Zhang, Liang |
| Author:
|
Tang, X. H. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
39-61 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we deal with the existence of periodic solutions of the $p(t)$-Laplacian Hamiltonian system $$ \begin {cases} \dfrac {{\rm d}}{{\rm d}t}(|\dot {u}(t)|^{p(t)-2}\dot {u}(t)) =\nabla F(t,u(t))\quad \text {a.e.} \ t\in [0,T] ,\\ u(0)-u(T)=\dot {u}(0)-\dot {u}(T)=0. \end {cases} $$ Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems. (English) |
| Keyword:
|
periodic solution |
| Keyword:
|
Hamiltonian system |
| Keyword:
|
$p(t)$-Laplacian system |
| Keyword:
|
critical point |
| Keyword:
|
minimax principle |
| Keyword:
|
least action principle |
| MSC:
|
34C25 |
| MSC:
|
37J45 |
| MSC:
|
58E50 |
| idZBL:
|
Zbl 1274.34129 |
| idMR:
|
MR3022768 |
| DOI:
|
10.1007/s10492-013-0002-x |
| . |
| Date available:
|
2013-01-23T10:11:43Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143134 |
| . |
| Reference:
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