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Infinitely many homoclinic solutions for a class of indefinite perturbed second-order Hamiltonian systems. (English) Zbl 1367.34052

The existence of homoclinic orbits is studied for the class of differential equations \[ -\ddot{u}(t)+L(t)u(t)=W_u(t,u(t))+G_u(t,u(t)). \] The existence of infinitely many homoclinic solutions is proven by using the theory of Bolle’s perturbation method in critical point. The paper reports some generalizations of known results.

MSC:

34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
34C14 Symmetries, invariants of ordinary differential equations
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