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

Pages: 778 - 787, Issue Special, July 2003

 Abstract        Full Text (194.1K)              

Addolorata Salvatore - Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125 Bari, Italy (email)

Abstract: 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:  Second order hamiltonian systems, loss of symmetry, multiplicity of homoclinic solutions, variational methods, perturbative arguments.
Mathematics Subject Classification:  34C37, 58E05, 70H05.

Received: September 2002;      Revised: March 2003;      Published: April 2003.