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Zbl 1221.37115
Daouas, Adel
Homoclinic orbits for superquadratic Hamiltonian systems without a periodicity assumption. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 11, 3407-3418 (2011). ISSN 0362-546X

Summary: We consider the second-order Hamiltonian system $\ddot q(t)+\nabla V(t,q(t))=f(t)$ where $V(t,q)= - K(t,q)+W(t,q)$. Under suitable conditions on the growth of $W$ and $K$, we establish the existence of a nontrivial homoclinic orbit without any assumption of periodicity on $V$. This homoclinic orbit is obtained as a limit of solutions of a certain sequence of nil-boundary-value problems which are obtained by the minimax methods.

MSC 2000:: *37J45 Periodic, homoclinic and heteroclinic orbits, etc.
34C37 Homoclinic and heteroclinic solutions of ODE
70H05 Hamilton's equations

Keywords: homoclinic orbit; Hamiltonian system; mountain pass theorem; the $(C)$ condition

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