Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials

Jian Ding; Junxiang Xu; Fubao Zhang
January 2009
Abstract & Applied Analysis;2009, Special section p1
Academic Journal
This paper concerns solutions for the Hamiltonian system: ˙ = ∂Hz(f,z). Here H(t,z) = (l/2)z • Lz + W(t, z), L is a 2N x 2N symmetric matrix, and W € C1 (R x R2N, R). We consider the case that 0 € σc(-(∂(d/dt) + L)) and W satisfies some superquadratic condition different from the type of Ambrosetti-Rabinowitz. We study this problem by virtue of some weak linking theorem recently developed and prove the existence of homoclinic orbits.


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