### Existence of periodic solutions of a class of third order delay differential equations in Banach spaces

CHEN Yu-jia, YANG He*

1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
• Received:2017-11-14 Online:2018-08-20 Published:2018-07-11

Abstract: Applying the monotone iterative method of upper and lower solutions, we discuss the existence of 2π-periodic solutions for the third-order differential equation with delays in ordered Banach space Eu(t)+M0u(t-τ0)=f(t,u(t), u(t-τ1), u(t-τ2)), t∈R,where f:R×E3→E is a continuous function which is 2π-periodic in t, and τ012 are positive constants. By establishing a new maximum principle, a monotone iterative procedure for the equation is constructed. Some existence and uniqueness results of 2π-periodic solutions for this equation are obtained.

CLC Number:

• O175.15
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