Homoclinic solutions for nonautonomous second order Hamiltonian systems with a coercive potential

[摘要] We shall be concerned with the existence of homoclinic solutions for the second order Hamiltonian system q - V-q (t, q) = f (t), where t is an element of R and q is an element of R. A potential V is an element of C-1 (R x R-n, R) is T-periodic in t, coercive in q and the integral of V (., 0) over [0, T] is equal to 0. A function f : R -> R-n is continuous, bounded, square integrable and f not equal 0. We will show that there exists a solution q(0) such that q(0)(t) -> 0 and q(0)(t) -> 0, as t -> +/- infinity. Although q equivalent to 0 is not a solution of our system, we are to call q(0) a homoclinic solution. It is obtained as a limit of 2kT-periodic orbits of a sequence of the second order differential equations. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-15

[关键词] coercive functional;homoclinic solutions;Hamiltonian systems;Palais-Smale condition