Homoclinics for asymptotically quadratic and superquadratic Hamiltonian systems. (English) Zbl 1168.58302

Summary: We find new conditions, which are different from those used in previous related studies, to ensure the existence of infinitely many homoclinic orbits for the second order Hamiltonian systems of the form \[ -\ddot q = V_q (t,q). \] Here, we assume that \(V(t,q)\) depends periodically on \(t\), and assume, on \(q\), that \(V(t,q)\) is asymptotically quadratic at \(q=0\) and is, as \(|q|\rightarrow \infty \), either asymptotically quadratic or superquadratic, as well as the new conditions.


58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
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