Infinitely many homoclinic solutions for second order Hamiltonian systems.(English)Zbl 1178.37063

Summary: We study the existence of infinitely many homoclinic solutions for second order Hamiltonian systems $$\ddot u -L(t)u+W_u(t,u) = 0,\forall t \in \mathbb R$$, where $$L(t)$$ is unnecessarily positive definite for all $$t \in \mathbb R$$, and $$W(t,u)$$ is of subquadratic growth as $$|u|\rightarrow \infty$$.

MSC:

 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 70H05 Hamilton’s equations
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References:

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