Volume no :19, Issue no: 1, February (2018)

Journal of Pure and Applied Mathematics: Advances and Applications

A STUDY OF POSITIVE PERIODIC SOLUTIONS FOR SECOND-ORDER DELAYED DIFFERENTIAL EQUATIONS

Author's: Yue Liang and Di Zhang
Pages: [47] - [60]
Received Date: February 27, 2018; Revised March 21, 2018
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100121933

Abstract

This paper deals with the existence of positive solutions for second-order differential equation with delay of the form



where is a constant, is a continuous function, is in is a constant which denotes the time delay. We first establish the positivity estimation for the linear equation. Then two existence theorems of positive solutions are obtained when f satisfies some inequality conditions. The discussion is based on the fixed point index theory in cones.

Keywords

second-order differential equation, positive solution, fixed point index, delay, existence.