Existence of Homoclinic Solutions for a Class of Second-Order Hamiltonian Systems with Locally Subquadratic Potentials

• Lv Xiang ^[1]
  1. [1] Shanghai Normal University

     Shanghai Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
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• Resumen

  • In this paper, we mainly consider the existence of homoclinic orbits for the following second-order Hamiltonian systems u¨(t)-L(t)u(t)+∇W(t,u(t))=f(t),where L(t) is a positive definite and symmetric matrix for all t∈R and the potential function W(t, u) is locally subquadratic. Here, the coefficient of the upper bound for W is a positive constant, whereas in the previous literature the corresponding coefficient need to be some integrable functions a(t) on R.