Periodic solutions for some nonautonomous p ( t ) -Laplacian Hamiltonian systems

Liang Zhang; X. H. Tang

Applications of Mathematics (2013)

  • Volume: 58, Issue: 1, page 39-61
  • ISSN: 0862-7940

Abstract

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In this paper, we deal with the existence of periodic solutions of the p ( t ) -Laplacian Hamiltonian system d d t ( | u ˙ ( t ) | p ( t ) - 2 u ˙ ( t ) ) = ∇ F ( t , u ( t ) ) a.e. t ∈ [ 0 , T ] , u ( 0 ) - u ( T ) = u ˙ ( 0 ) - u ˙ ( T ) = 0 . 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.

How to cite

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Zhang, Liang, and Tang, X. H.. "Periodic solutions for some nonautonomous $p(t)$-Laplacian Hamiltonian systems." Applications of Mathematics 58.1 (2013): 39-61. <http://eudml.org/doc/251426>.

@article{Zhang2013,
abstract = {In this paper, we deal with the existence of periodic solutions of the $p(t)$-Laplacian Hamiltonian system \[ \{\left\lbrace \begin\{array\}\{ll\} \dfrac\{\{\rm d\}\}\{\{\rm d\}t\}(|\dot\{u\}(t)|^\{p(t)-2\}\dot\{u\}(t)) =\nabla F(t,u(t))\quad \text\{a.e.\} \ t\in [0,T] ,\\ u(0)-u(T)=\dot\{u\}(0)-\dot\{u\}(T)=0. \end\{array\}\right.\} \] 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.},
author = {Zhang, Liang, Tang, X. H.},
journal = {Applications of Mathematics},
keywords = {periodic solution; Hamiltonian system; $p(t)$-Laplacian system; critical point; minimax principle; least action principle; periodic solution; Hamiltonian system; -Laplacian system; critical point; minimax principle; least action principle},
language = {eng},
number = {1},
pages = {39-61},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Periodic solutions for some nonautonomous $p(t)$-Laplacian Hamiltonian systems},
url = {http://eudml.org/doc/251426},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Zhang, Liang
AU - Tang, X. H.
TI - Periodic solutions for some nonautonomous $p(t)$-Laplacian Hamiltonian systems
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 1
SP - 39
EP - 61
AB - In this paper, we deal with the existence of periodic solutions of the $p(t)$-Laplacian Hamiltonian system \[ {\left\lbrace \begin{array}{ll} \dfrac{{\rm d}}{{\rm d}t}(|\dot{u}(t)|^{p(t)-2}\dot{u}(t)) =\nabla F(t,u(t))\quad \text{a.e.} \ t\in [0,T] ,\\ u(0)-u(T)=\dot{u}(0)-\dot{u}(T)=0. \end{array}\right.} \] 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.
LA - eng
KW - periodic solution; Hamiltonian system; $p(t)$-Laplacian system; critical point; minimax principle; least action principle; periodic solution; Hamiltonian system; -Laplacian system; critical point; minimax principle; least action principle
UR - http://eudml.org/doc/251426
ER -

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