Discussion On The Boundary Value Problem Of Several Classes Of Differential Equations

In this paper, by using the cone theory, the topological degree theory, the critical point theory, we study the existence and multiplicity of solutions to several kinds of second-order differential equations. Some new results are obtained, some relevant results are extended and improved. The structure of this paper as follows.In the first chapter, we introduce the background of the discussed problem of this thesis briefly, and we state the main results of this thesis concretely.In the second chapter, by using the improved Amann's three-solution theorem, we investigate the periodic boundary value problems of second-order nonlinear differential equation The sufficient conditions for the existence of three solutions are obtained, an example is presented to illustrate the application of the obtained results.In the third chapter, by using a new fixed point theorem of u 0-concave operator, we study the periodic boundary value problem of second-order impulsive differential equation Where , the existence of solutions is obtained. An example is given to illustrate the application of the obtained results.In the fourth chapter, we discussed the second-order impulsive differential equation two-point BVP Where ,tm.We obtain that the problem has unique solution by using a new fixed point theorem of u 0-concave operator.In the fifth chapter, by using the critical point theory, we study the second order two-point boundary value problems the existence of solutions is obtained. An example is given to illustrate the application of the obtained results.