Homoclinic orbits of superlinear Hamiltonian systems

Chen, Guanwei; Ma, Shiwang

doi:10.1090/S0002-9939-2011-11185-7

Homoclinic orbits of superlinear Hamiltonian systems
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by Guanwei Chen and Shiwang Ma PDF

Proc. Amer. Math. Soc. 139 (2011), 3973-3983 Request permission

Abstract:

In this paper, we consider the first-order Hamiltonian system \[ J\dot {u}(t)+\nabla H(t,u(t))=0,\quad t\in \mathbb {R}. \] Here the classical Ambrosetti-Rabinowitz superlinear condition is replaced by a general super-quadratic condition. We will study the homoclinic orbits for the system. The main idea here lies in an application of a variant generalized weak linking theorem for a strongly indefinite problem developed by Schechter and Zou.

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