Abstract
In this paper we consider the existence of homoclinic solutions for the following second-order non-autonomous Hamiltonian system: (HS) q ̈ − L ( t ) q + W q ( t , q ) = 0 , where L ( t ) ∈ C ( R , R n 2 ) is a symmetric and positive definite matrix for all t ∈ R , W ( t , q ) = a ( t ) | q | γ with a ( t ) : R → R + is a positive continuous function and 1 < γ < 2 is a constant. Adopting some other reasonable assumptions for L and W , we obtain a new criterion for guaranteeing that (HS) has one nontrivial homoclinic solution by use of a standard minimizing argument in critical point theory. Recent results from the literature are generalized and significantly improved.
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