#### Zhibo Cheng, Yun Xin, Periodic solutions for fourth-order neutral differential equations with linear autonomous difference operators, Vol. 2017 (2017), Article ID 29, pp. 1-21

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DOI: 10.23952/jnfa.2017.29

Received January 23, 2017; Accepted May 4, 2017; Published May 15, 2017

Abstract. In this article, we discuss the properties of linear autonomous difference operator $(Ax)(t)=x(t)-c(t) x(t-\delta(t))$. By applying the Green’s function of fourth-order differential equations and a fixed point theorem in cones, we obtain some sufficient conditions for the existence, nonexistence, multiplicity of positive periodic solutions for a generalized fourth-order neutral differential equation with variable parameters.