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Infinitely many homoclinic solutions for a class of damped vibration problems

In this paper, we deal with the existence of infinitely many homoclinic solutions for the damped vibration problems ü(t)+Au̇(t)−L(t)u(t)+∇W(t,u(t))=0, where A is an antisymmetry N × N constant matrix, we establish some new existence results to guarantee that the above system has infinitely many homoclinic solutions under more relaxed assumptions on W(t,x), which satisfies a kind of new subquadratic condition by using fountain theorem. Recent results in the literature are generalized and significantly improved. Copyright © 2013 John Wiley & Sons, Ltd.