Infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems

2015/01/26 by Lv, Xiang
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.06557

Abstract

In this paper, we mainly consider the existence of infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems u-L(t)u+W_u(t,u)=0, where L(t) is not necessarily positive definite and the growth rate of potential function W can be in (1,3/2). Using the variant fountain theorem, we obtain the existence of infinitely many homoclinic solutions for the second-order Hamiltonian systems.

Related

• Existence and multiplicity of Homoclinic solutions for the second order Hamiltonian systems
• On a class of singular second-order Hamiltonian systems with infinitely many homoclinic solutions
• New homoclinic orbits for Hamiltonian systems with asymptotically quadratic growth at infinity
• On the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems
• Infinitely many homoclinic orbits for a class of superquadratic Hamiltonian systems