Electron. J. Differential Equations, Vol. 2019 (2019), No. 47, pp. 1-12.

Periodic solutions of second-order non-autonomous dynamical systems with vanishing Green's functions

Yongxin Jiang

In this article, we study the existence and multiplicity of positive periodic solutions for second-order non-autonomous dynamical systems when Green's functions are non-negative. The proofs are based on a nonlinear alternative principle of Leray-Schauder and the fixed point theorem in cones. Some recent results in the literature are generalized and improved.

Submitted March 18, 2018. Published April 10, 2019.
Math Subject Classifications: 34C25, 34B15, 34A25.
Key Words: Vanishing Green's function; Leray-Schauder alternative; fixed point theorem in cones

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Yongxin Jiang
Department of Mathematics
Hohai University
Nanjing 210098, China
email: yxinjiang@hhu.edu.cn

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