Existence And Multiplicity Of Solutions For Two Classes Of Boundary Value Problem Of Impulsive Differential Systems

Due to the close relation with many problems in the physical, chemical, biological, economic and other fields, the existence and multiplicity of solutions for the boundary value problem of differential equations have become an important research topic. In this thesis, we constructed variational structures for a class of impulsive Hamiltonian system and p-Laplacian system respectively, investiged boundary value problem of these two systems by using the critial point theory, and the suffcient conditions of existence of at least one solution or infinitely many solutions are obtained. The thesis consists of four chapters.In chapter1, we introduced the current research background and status, some prepare knowledges of the critical point theory. Our works are also stated briefly.In chapter2, we studied the existence and multiplicity of solutions for a class of second-order impulsive Hamiltonian system by using a even functional theorem. We give some new criteria to guarantee that the system have at least one solution or infinitely many solutions when F(t,u) is subquadratics, asymptotically quadratic and superquadratics, and extend some existing results; moreover, we give two examples to verify the effectiveness of the conclusions.In chapter3, by using the variant fountain theorem, we studied the multiplicity of solutions for a class of second-order impulsive p-Lapl-acian system. Some new criteria are obtained to guarantee that the impulsive problem has infinitely many solutions when the impulsive functions satisfy superlinear or sublinear conditions, and some existing results are improved; furthermore, two examples are presented to illustrate the conclusions. Finally, in chapter4, we made some summery and outlook briefly for this thesis.