We prove the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems in ℝN of the form q̈ = q - W1(t,q), where we assume the existence of a sequence (tn) ⊂ ℝ such that tn → ± ∞ and W1(t +tn,x) → W1(t,x) as n → ± ∞ for any (t,x) ε ℝ × ℝN. Moreover, under a suitable non degeneracy condition, we prove that this class of systems admits multibump solutions.
Montecchiari, P., Nolasco, M., Terracini, S. (1997). Multiplicity of homoclinics for a class of time recurrent second order Hamiltonian systems. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 5(6), 523-555 [10.1007/s005260050078].
Multiplicity of homoclinics for a class of time recurrent second order Hamiltonian systems
TERRACINI, SUSANNA
1997
Abstract
We prove the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems in ℝN of the form q̈ = q - W1(t,q), where we assume the existence of a sequence (tn) ⊂ ℝ such that tn → ± ∞ and W1(t +tn,x) → W1(t,x) as n → ± ∞ for any (t,x) ε ℝ × ℝN. Moreover, under a suitable non degeneracy condition, we prove that this class of systems admits multibump solutions.
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