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Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials. (English) Zbl 0744.34045
The goal of this paper is to establish the existence of infinitely many homoclinic orbits for a class of second order Hamiltonian systems of the form (HS) $\ddot q-L(t)q+V\sb q(t,q)=0$ under suitable assumptions, in particular $V\in C\sp 2$ ($\bbfR\times\bbfR\sp n,\bbfR$) is of kind “superquadratic”. The approach to (HS) involves the use of variational methods of a minimax nature and the authors seek solutions of (HS) as critical points of the functional $I$ defined on $W\sp{1,2}(\bbfR;\bbfR\sp n)$ by $I(q)=\int\sp \infty\sb{-\infty}({1\over 2}\vert \dot q(t)\vert\sp 2+L(q)q.q-V(t,q))dt$.

34C37Homoclinic and heteroclinic solutions of ODE
58E99Variational problems in infinite-dimensional spaces
37-99Dynamic systems and ergodic theory (MSC2000)
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