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Heteroclinic solutions for a class of the second order Hamiltonian systems. (English) Zbl 1117.37033
Summary: We are concerned with the existence of heteroclinic orbits for the second-order Hamiltonian system q ¨+V q (t,q)=0, where q n and VC 1 (× n ,), V0. We will assume that V and a certain subset n satisfy the following conditions. is a set of isolated points and #2. For every sufficiently small ε>0 there exists δ>0 such that for all (t,z)× n , if d(z,)ε then -V(t,z)δ. The integrals - -V(t,z)dt, z, are equibounded and -V(t,z), as |t|, uniformly on compact subsets of n . Our result states that each point in is joined to another point in by a solution of our system.
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
58E05Abstract critical point theory
34C37Homoclinic and heteroclinic solutions of ODE
70H05Hamilton’s equations