Positive Solutions Of Periodic Boundary Value Problems For Second Order Impulsive Differential Equations

In mordern technology areas of practial problems, impulse as an instantaneaus catastrophe phenomenon is universal existence. Recentlly some new technology achievement has been proved that impulsive system universally existed in aeromautics,informatics,cybernetics,communicats,biology,medicine,economics areas.In this paper, we are devoted to establish the multiplicity of positive solutions to superlinear attractive singular equations with periodic boundary conditions. This paper is composed of four parts. In the first chapter, we introduce the historical background of the problems which will be investigated and the main results of this paper. In the second chapter, we proof a general existence principle for the Periodic Boundary Value Problems, which will be used in chapter three. In the third chapter,it deals with the following multiple positive solutions of boundary value problems for second order impulsive differential equations by the fixed point theorem in cones.It is proved that such a problem has at least two positive solutions under our reasonable conditions. Our nonlinearity may be singular in its dependent variable and superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones. The Green Function is also important in the proof. The forth partis an example, the example is given to explain the main results.