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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) $$\ddot q-L(t)q+V_ q(t,q)=0$$ under suitable assumptions, in particular $$V\in C^ 2$$ ($$\mathbb{R}\times\mathbb{R}^ n,\mathbb{R}$$) 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 $$W^{1,2}(\mathbb{R};\mathbb{R}^ n)$$ by $$I(q)=\int^ \infty_{-\infty}({1\over 2}| \dot q(t)|^ 2+L(q)q.q-V(t,q))dt$$.
Reviewer: P.Bolley (Nantes)

##### MSC:
 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 58E99 Variational problems in infinite-dimensional spaces 37-XX Dynamical systems and ergodic theory
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