Electron. J. Diff. Equ., Vol. 2013 (2013), No. 151, pp. 1-11.

Multiplicity of homoclinic solutions for second-order Hamiltonian systems

Gui Bao, Zhiqing Han, Minghai Yang

Abstract:
By using a modified function technique and variational methods, we establish the existence of infinitely many homoclinic solutions for a second-order Hamiltonian system $\ddot{u}-L(t)u+F_u(t,u)=0$, for all t in R, where no coercive condition for F(t,u) at infinity is imposed.

Submitted January 4, 2013. Published June 28, 2013.
Math Subject Classifications: 37J45, 58E05, 34C37, 70H05.
Key Words: Second order Hamilton system; Homoclinic solution; variational method.

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Gui Bao
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: baoguigui@163.com
Zhiqing Han
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: hanzhiq@dlut.edu.cn
Minghai Yang
Department of Mathematics
Xinyang Normal University
Xinyang 464000, China
email: ymh1g@126.com

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