New existence and multiplicity of homoclinic solutions for second order non-autonomous systems

作者：Chen, Huiwen; He, Zhimin^*

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2014, (22): 1-18.

DOI：10.14232/ejqtde.2014.1.22

• non-autonomous systems
• homoclinic solutions
• variational methods
• mountain pass theorem
• fountain theorem

In this paper, we study the second order non-autonomous system u(t) + Au(t) - L(t)u(t) + del W(t,u(t)) = 0, for all t is an element of R, where A is an antisymmetric N x N constant matrix, L is an element of C (R,R-N x N) may not be uniformly positive definite for all t is an element of R, and W(t, u) is allowed to be sign-changing and local superquadratic. Under some simple assumptions on A, L and W, we establish some existence criteria to guarantee that the above system has at least one homoclinic solution or infinitely many homoclinic solutions by using the mountain pass theorem or the fountain theorem, respectively. Recent results in the literature are generalized and significantly improved.

• 出版日期2014
• 单位中南大学