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A note on homoclinic orbits for second order Hamiltonian system

Authors:

Institution:

(1) Department of Mathematics, Zhejiang University, 310027 Hangzhou;(2) Department of Mathematics, China University of Science and Technology,m, 230026 Hefei

Abstract:

Some existence and multiplicity of homoclinic orbits for second order Hamiltonian system

$\ddot x - a(t)x + f(t,x) = 0$

are given by means of variational methods, where the function $- \frac{1}{2}a(t)|s|^2 + \int_0^s {f(t,s)ds{\text{ is}}}$ is asymptotically quadratic in s at infinity and subquadratic in s at zero, and the function a(t) mainly satisfies the growth condition

$\begin{array}{*{20}c} {\lim } \\ {t \to \infty } \\ \end{array} \int_t^{t + 1} {a(t)dt = + \infty ,\forall l \in R} ^1 .$

A resonance case as well as a noncompact case is discussed too. This work is partially supported by the Associateship Scheme of ICTP, by the National Natural Science Foundation of China and by the Zhejiang Natural Science Foundation.

Keywords:

1991 MR Subject Classification" target="_blank">1991 MR Subject Classification 34A34 34C37 46N20

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