Homoclinic solutions for singular Hamiltonian systems without the strong force condition

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Antabli, Mohamed¹  Boughariou, Morched¹ 

[1] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Lab EDP LR03ES04, Tunis 2092, Tunisia

关键词: Singular Hamiltonian system;    Strong-force condition;    Homoclinic solution;    Minimax methods;    Morse theory;   

DOI  :  10.1016/j.jmaa.2018.11.028

来源: Elsevier

【 摘 要 】

We consider the existence of homoclinic orbits at the origin of a Hamiltonian system q + V'(q) = 0 in R-N (N >= 3) where V has a strict global maximum at q = 0 and a singularity at a point e not equal 0, namely V(q) -> -infinity as q -> e. We establish via variational methods the existence of a generalized homoclinic orbit (q) over bar that may enter the singularity e without assuming the strong force condition of Gordon. Moreover when V similar to -1/vertical bar q - e vertical bar(alpha) (0 < alpha < 2) near e, we give a bound for the number of collisions of based on the Morse index of approximated solutions. As a consequence we obtain that-4, is classical (non-collision) orbit for alpha is an element of ]1, 2[ and enters the singularity e at most one time in R if alpha is an element of]0, 1]. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free