Homoclinic solutions for a class of non-periodic second order Hamiltonian systems

Jian Ding, Southeast University, Nanjing, P. R. China
Junxiang Xu, Southeast University, Nanjing, P. R. China
Fubao Zhang, Southeast University, Nanjing, P. R. China

E. J. Qualitative Theory of Diff. Equ., No. 31. (2010), pp. 1-11.

Abstract: We study the existence of homoclinic solutions for the second order Hamiltonian system $\ddot{u}+V_{u}(t,u)=f(t)$. Let $V(t,u)=-K(t,u)+W(t,u)\in C^{1}(\mathbb{R}\times\mathbb{R}^{n}, \mathbb{R})$ be $T$-periodic in $t$, where $K$ is a quadratic growth function and $W$ may be asymptotically quadratic or super-quadratic at infinity. One homoclinic solution is obtained as a limit of solutions of a sequence of periodic second order differential equations.

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