Homoclinic orbits of first-order superquadratic Hamiltonian systems

2013/04/20 by Cyril J. Batkam, Batkam, Cyril J.
Mathematics · #35B38 #37J45 #70H05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B38 #msc:37J45 #msc:70H05

paper · pdf · doi:10.48550/arxiv.1304.5647

17 pages

arxiv created 2013/04/20 · arxiv updated 2013/04/23

Abstract

In this article, we study the existence of homoclinic orbits for the first-order Hamiltonian system equation* Ju(t)+∇ H(t,u(t))=0, t∈ℝ. equation* Under the Ambrosetti-Rabinowitz's superquadraticy condition, or no Ambrosetti-Rabinowitz's superquadracity condition, we present two results on the existence of infinitely many large energy homoclinic orbits when H is even in u. We apply the generalized (variant) fountain theorems due to the author and Colin. Under no Ambrosetti-Rabinowitz's superquadracity condition, we also obtain the existence of a ground state homoclinic orbit by using the method of the generalized Nehari manifold for strongly indefinite functionals developed by Szulkin and Weth.

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