Three positive periodic solutions of second order nonlinear neutral functional differential equations with delayed derivative

Advances in Difference Equations

article

Yang, He¹  Zhang, Lu¹ 

[1] College of Mathematics and Statistics, Northwest Normal University

关键词: Neutral functional differential equation;    Positive periodic solution;    Delayed derivative;    Cone;    Leggett–Williams fixed point theorem;   

DOI  :  10.1186/s13662-020-02630-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper deals with the existence of three positive periodic solutions for a class of second order neutral functional differential equations involving the delayed derivative term in nonlinearity $(x(t)-cx(t-\delta)){''}+a(t)g(x(t))x(t)=\lambda b(t)f(t,x(t),x(t-\tau_{1}(t)),x'(t-\tau_{2}(t)))$. By utilizing the perturbation method of positive operator and Leggett–Williams fixed point theorem, a group of sufficient conditions are established.

【 授权许可】

CC BY