Multiple homoclinic orbits for a class of second order perturbed Hamiltonian systems

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2003, 2003(Special): 778-787. doi: 10.3934/proc.2003.2003.778

Multiple homoclinic orbits for a class of second order perturbed Hamiltonian systems

1.	Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125 Bari

Received September 2002 Revised March 2003 Published April 2003

Abstract
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We look for homoclinic orbits of the system of differential equations

$- dot(q) + L(t)q = V_q(t, q) + g(t)$

where $V : R \times R^N (\to) R$ is superquadratic and even in $q$ and $L(t)$ is a a symmetric, positive definite matrix. If $g(t) != 0$, in spite of the loss of symmetry a suitable perturbative method allows one to state the existence of infinitely many solutions of the problem.

Keywords: loss of symmetry, Second order hamiltonian systems, perturbative arguments., variational methods, multiplicity of homoclinic solutions.

Mathematics Subject Classification: 34C37, 58E05, 70H0.

Citation: Addolorata Salvatore. Multiple homoclinic orbits for a class of second order perturbed Hamiltonian systems. Conference Publications, 2003, 2003 (Special) : 778-787. doi: 10.3934/proc.2003.2003.778

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