The Existence Of Solutions To Some Kinds Of Nonlinear Problem

Differential equations and integral equations are two very important and closely linked branches of calculus. Differential equations play an important role in many disciplines, so the study of differential equation solution seems to be very important. But it is difficult to consider solutions of some kind of differential equations directly, we need transform differential equations into corresponding integral equations and consider integral equations using the fixed point theory.This paper mainly studied the existence of solutions to some kinds of differential equations, and the fixed point to a kind of integral equation system. This paper contains five chapter:The first chapter is the introduction of this paper. It mainly introduces the back-ground and some basic method of this paper.In chapter two, applying fixed point index theory, the existence of positive solution to singular second-order boundary value problem is considered.The third chapter, fixed point for systems of nonlinear Hammerstein integral equations is obtained by using fixed point index theory. An example is worked out to illustrate the main result.In chapter four, the existence of positive solutions for a system of generalized Lidstone problem is considered using fixed point index theory. The last chapter, by using a generalized Leggett-Williams theory, the existence of triple solutions for a fractional differential equation is considered.