Several Classes Of Nonlinear Pulse Equation And Its Application

Along with the development of modern physics and applied mathematics,many kinds of non-linear problems have emerged, which greatly urge the nonlinearfunctional analysis to be better improved. Non-linear impulsive equation is amore important branch of non-linear functional analysis. Because the impulsiveequations have the impulsive phenomenon and the continuous of the solutions isafected by the qualities of impulsive, using the method of nonlinear analysis tostudy nonlinear impulsive equations is valuable questions. In this paper by usingfixed point theorem, we discuss several classes of nonlinear impulsive equationsand give some sufcient conditions of the existences of solutions. Meanwhile, weapply the main results to the existence of solutions for boundary value problemsand initial value problems.The thesis is divided into three chapters.In Chapter1, we study the following second-order impulsive Sturm-Liouvilleboundary value problemIn abstract space, by the fixed point theory for strict set contraction operators,we obtain the existence of solutions for the boundary value problems. The resultswe obtained improve and extend known results. Finally, we give an example inBanach Spaces to demostrare the main results of this paper.In Chapter2, we study the following Sturm-Liouville problems with integralboundary conditions for second order impulsive diferential equations on the half- By usingthe Leggett-Williams fixed point theorem, we obtain the existence theorems ofat least three positive solutions for the boundary value problems. The results weobtained improve and extend known results.In Chapter3, we consider a class of nonlinear n th order impulsive integro-diferential equations of mixed type in Banach SpaceBy use of a comparison result and the Mo¨nch fixed point theorem, we obtain theexistence of solutions of the initial value problem.