The Existence On Positive Solutions Of Impulsive Boundary Value Problem For First-order Nonlinear Functional Differential Equations

Impulsive differential equations are recognized as an excellent source of models tosimulate processes and phenomena observed in control theory, physics, chemistry,population dynamics, biotechnology, industrial robotics, optimal control, etc., and area basic tool for studying evolution processes that are subject to abrupt changes in theirstates. The study of impulsive boundary value problem of first-order nonlinearfunctional differential equations is more fundamental function.In this paper, we first introduce the context and significance of impulsive boundaryvalue problem of the nonlinear functional differential equations studied, and provesome lemmas which are used in the paper. Next, we consider the existence on positivesolutions of impulsive boundary value problem of the following first-order nonlineardifferential equationsome analysis techniques, we get some sufficient conditions which guarantee theexistence of one positive solution for the above impulsive boundary value problems.Further more, we consider the existence of multiple positive solutions for the aboveimpulsive boundary value problem. And we obtain some new results on the existenceof multiple positive solutions for the impulsive boundary value problems. Our resultsgeneralize and improve the relative results of the paper [9]. In addition, our resultsshow that positive solutions for the impulsive boundary value problems may beyielded completely by some proper impulsive conditions, and also implies that properimpulsive conditions are of great significance to simulate processes, optimal control, population model and so on.