We consider a class of second order Hamiltonian systems $\ddot q=q-V'(t,q)$ where $V(t,q)$ is asymptotic at infinity to a time periodic and superquadratic function $V_+(t,q)$. We prove the existence of a class of multibump solutions whose $\omega$-limit is a suitable homoclinic orbit of the system at infinity $\ddot q=q-V'_+(t,q)$.
Asymptotic behavior for a class of multibump solutions to Duffing-like systems
CALDIROLI, Paolo;
1995-01-01
Abstract
We consider a class of second order Hamiltonian systems $\ddot q=q-V'(t,q)$ where $V(t,q)$ is asymptotic at infinity to a time periodic and superquadratic function $V_+(t,q)$. We prove the existence of a class of multibump solutions whose $\omega$-limit is a suitable homoclinic orbit of the system at infinity $\ddot q=q-V'_+(t,q)$.
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