Existence of Nonoscillatory Solutions of First Order Non-Linear Neutral Differential Equations

Abstract

In this paper, some sufficient conditions have been obtained for the existence of positive solutions of the first order nonlinear neutral differential equations bounded by a ratio of bounded functions. For this purpose we used Krasnoselskii’s fixed point theorem and Lebesgue’s dominated convergence theorem to establish new sufficient conditions for the existence of nonoscillatory positive solutions. An example is included to illustrate the main result.