| Title:
|
Existence of solutions for a class of second-order $p$-Laplacian systems with impulsive effects (English) |
| Author:
|
Chen, Peng |
| Author:
|
Tang, Xianhua |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
59 |
| Issue:
|
5 |
| Year:
|
2014 |
| Pages:
|
543-570 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to study the existence and multiplicity of a periodic solution for the non-autonomous second-order system \begin {gather} \frac {{\rm d}}{{\rm d}t}(|\dot {u}(t)|^{p-2}\dot {u}(t)) =\nabla F(t, u(t)),\quad \text {\rm a.e.}\ t\in [0,T],\nonumber \\ u(0)-u(T)=\dot {u}(0)-\dot {u}(T)=0,\nonumber \\ \Delta \dot {u}^i(t_{j})=\dot {u}^i(t_j^+)-\dot {u}^i(t_j^-)=I_{ij}(u^i(t_j)),\ i = 1, 2,\dots , N;\ j = 1, 2,\dots ,m.\nonumber \end {gather} By using the least action principle and the saddle point theorem, some new existence theorems are obtained for second-order $p$-Laplacian systems with or without impulse under weak sublinear growth conditions, improving some existing results in the literature. (English) |
| Keyword:
|
second-order $p$-Laplacian Hamiltonian systems |
| Keyword:
|
impulsive effect |
| Keyword:
|
critical point theory |
| MSC:
|
34B15 |
| MSC:
|
34B37 |
| MSC:
|
34C25 |
| MSC:
|
58E30 |
| MSC:
|
58E50 |
| idZBL:
|
Zbl 06391450 |
| idMR:
|
MR3255795 |
| DOI:
|
10.1007/s10492-014-0071-5 |
| . |
| Date available:
|
2014-09-29T09:01:14Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143930 |
| . |
| Reference:
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