Infinitely many homoclinic orbits for supperlinear Hamiltonian systems

Jun Wang, Junxiang Xu, Fubao Zhang

Abstract


In this paper we study the first order nonautonomous Hamiltonian system
$$
\dot{z}=\mathcal J H_{z}(t,z),
$$
where $H(t,z)$ depends periodically on $t$. By using a generalized
linking theorem
for strongly indefinite functionals, we prove that the system has
infinitely many homoclinic orbits for weak superlinear cases.

Keywords


Homoclinic orbits; Hamiltonian systems; (C)_c-condition; variational methods

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