Abstract
The existence of homoclinic orbits is obtained for a class of the second order Hamiltonian systems u ̈ ( t ) − L ( t ) u ( t ) + ∇ W ( t , u ( t ) ) = 0 , ∀ t ∈ R , by the local linking lemma, where W ( t , x ) is superquadratic and need not be nonnegative globally.
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