On periodic solutions of non-autonomous second order Hamiltonian systems

Xingyong Zhang; Yinggao Zhou

Applications of Mathematics (2010)

  • Volume: 55, Issue: 5, page 373-384
  • ISSN: 0862-7940

Abstract

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The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system 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 the least action principle.

How to cite

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Zhang, Xingyong, and Zhou, Yinggao. "On periodic solutions of non-autonomous second order Hamiltonian systems." Applications of Mathematics 55.5 (2010): 373-384. <http://eudml.org/doc/38134>.

@article{Zhang2010,
abstract = {The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system \begin\{equation*\} \{\left\lbrace \begin\{array\}\{ll\} \ddot\{u\}(t)=\nabla F(t,u(t)),\hspace\{5.0pt\}\text\{a.e.\} \ t\in [0,T],\\ u(0)-u(T)=\dot\{u\}(0)-\dot\{u\}(T)=0. \end\{array\}\right.\} \end\{equation*\} Some new existence theorems are obtained by the least action principle.},
author = {Zhang, Xingyong, Zhou, Yinggao},
journal = {Applications of Mathematics},
keywords = {periodic solution; critical point; non-autonomous second-order system; Sobolev inequality; periodic solution; critical point; non-autonomous second-order system; Sobolev inequality},
language = {eng},
number = {5},
pages = {373-384},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On periodic solutions of non-autonomous second order Hamiltonian systems},
url = {http://eudml.org/doc/38134},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Zhang, Xingyong
AU - Zhou, Yinggao
TI - On periodic solutions of non-autonomous second order Hamiltonian systems
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 5
SP - 373
EP - 384
AB - The purpose of this paper is to study the existence of periodic solutions for the non-autonomous second order Hamiltonian system \begin{equation*} {\left\lbrace \begin{array}{ll} \ddot{u}(t)=\nabla F(t,u(t)),\hspace{5.0pt}\text{a.e.} \ t\in [0,T],\\ u(0)-u(T)=\dot{u}(0)-\dot{u}(T)=0. \end{array}\right.} \end{equation*} Some new existence theorems are obtained by the least action principle.
LA - eng
KW - periodic solution; critical point; non-autonomous second-order system; Sobolev inequality; periodic solution; critical point; non-autonomous second-order system; Sobolev inequality
UR - http://eudml.org/doc/38134
ER -

References

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  8. Tang, C. L., 10.1016/S0362-546X(97)00493-8, Nonlinear Anal., Theory Methods Appl. 32 (1998), 299-304. (1998) Zbl0949.34032MR1610641DOI10.1016/S0362-546X(97)00493-8
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