The Extend And Applicance Of Several Fixed Point Theorems

Recently, the questions of the existence of positive solutions of nonlinear conjugate boundary value have been attached much attention by many scholars, in which the new fields are brought by the physics engineering and the domain of chemistry. In chapter 2 of this thesis, the author considers the positive solution of the (k, n-k) conjugate boundary value problems and discusses the following equation: where h(x) may be singular when x=0 and x=1. The existence of positive solutions is obtained in the paper for nonlinear conjugate boundary value problem by means of the extended fixed point theorem concerning cone compression and expansion. The conclusions extend and improve the main results of Zhang Guowei and other authors.In chapter 3 of this thesis, the author brings out the theorem of convex function's domain expansion and compression fixed point theorem. The author improves Zhang Guowei and other authors'conditions and does not use the tradition linear-space's retract but use other brief means spread thetheorems of Zhang Guowei and Sun Jingxian.In chapter 4 of this thesis, the author extends the character of the abstract differentiabi-lity spaces from the finity to the infinity. The author combines the measure of noncompactness and gives another fixed point theorem and uses it to obtain the existence of the terminal value problem about the differential equation.