On The Research Of Solutions Of Several Kinds Of Nonlinear Diferential Equation And Systems

Along with the development of science and technology, various non-linear problemshave aroused people’s widespread interest day by day, and so the nonlinear analysishas become one important research direction in modern mathematics. The nonlinearfunctional analysis is an important branch in nonlinear analysis, because it can wellexplain the various natural phenomenon. The boundary value problem of nonlineardiferential equation stems from the applied mathematics, the physics, the cyberneticsand each kind of application discipline. It is one of the most active domains of functionalanalysis studies at present. The nonlinear diferential equation (systems) with non-localboundary value problems and with mixed boundary value problems have become a hotspot. In this paper, we employ the cone theory and the topological degree theoryto study several kinds of boundary value problems for nonlinear diferential equation(systems) and obtain some new results.The thesis is divided into three sections according to contents.Chapter1In this chapter we use topological degree theory and the first eigenval-ue corresponding to the revelent linear operator to investigate the following non-localboundary value problems In this chapter, we make a special set to overcome the problems brought by the Greenfunction and get the nontrivial solutions.Chapter2In this chapter we consider the following equation systems problemswith Sturm-Liouville boundary value Chapter3Based on the above two chapters, in this chapter we discuss the dif-ferential equation problems for changing sign non-linear itemsthis chapter, we employ the cone fixed theory to get the solutions of existence for theequation systems.