Existence of solutions for a class of second-order p -Laplacian systems with impulsive effects

Peng Chen; Xianhua Tang

Applications of Mathematics (2014)

  • Volume: 59, Issue: 5, page 543-570
  • ISSN: 0862-7940

Abstract

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The purpose of this paper is to study the existence and multiplicity of a periodic solution for the non-autonomous second-order system d d t ( | u ˙ ( t ) | p - 2 u ˙ ( t ) ) = ∇ F ( t , u ( t ) ) , a.e. t ∈ [ 0 , T ] , u ( 0 ) - u ( T ) = u ˙ ( 0 ) - u ˙ ( T ) = 0 , Δ u ˙ i ( t j ) = u ˙ i ( t j + ) - u ˙ i ( t j - ) = I i j ( u i ( t j ) ) , i = 1 , 2 , ⋯ , N ; j = 1 , 2 , ⋯ , m . 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.

How to cite

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Chen, Peng, and Tang, Xianhua. "Existence of solutions for a class of second-order $p$-Laplacian systems with impulsive effects." Applications of Mathematics 59.5 (2014): 543-570. <http://eudml.org/doc/262041>.

@article{Chen2014,
abstract = {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.},
author = {Chen, Peng, Tang, Xianhua},
journal = {Applications of Mathematics},
keywords = {second-order $p$-Laplacian Hamiltonian systems; impulsive effect; critical point theory; second-order $p$-Laplacian Hamiltonian systems; impulsive effect; critical point theory},
language = {eng},
number = {5},
pages = {543-570},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of solutions for a class of second-order $p$-Laplacian systems with impulsive effects},
url = {http://eudml.org/doc/262041},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Chen, Peng
AU - Tang, Xianhua
TI - Existence of solutions for a class of second-order $p$-Laplacian systems with impulsive effects
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 5
SP - 543
EP - 570
AB - 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.
LA - eng
KW - second-order $p$-Laplacian Hamiltonian systems; impulsive effect; critical point theory; second-order $p$-Laplacian Hamiltonian systems; impulsive effect; critical point theory
UR - http://eudml.org/doc/262041
ER -

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