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Zhang, Qingye; Liu, Chungen

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

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 2, 894-903 (2010).
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 \(|u|\rightarrow \infty \).

Cited in 50 Documents

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

Keywords:

homoclinic solution; second order Hamiltonian system; subquadratic
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\textit{Q. Zhang} and \textit{C. Liu}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 2, 894--903 (2010; Zbl 1178.37063)
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