Singular Differential Equations, Difference Equations And Differential - Integral Equation Solution

This paper contains four sections.Section one is the introduction, which summarizes the main results of this paper.In section two, we investigate nonresnonance singular Dirichlet boundary value problem* of the formWe get the existence of (7[0,1] positive solutions of BVP(l) and eigen-functions when A = 1 in BVP(l). These rfcouiia , ' ind improve results of [19,20,44].In section three, we study positive solutions of third-order difference equation boundary value problems of the formWe obtain the existence theorem wutn /is semilinear. The mainresults of this paper improve and include results of [28,29]. At the same time, we also get the existence of positive solutions of equationThe result extend those of [28,30],In the last section, we research the global solutions of initial value problem for nonlinear differential-integro equations of mixed type in Banach space of the formwhere T fa an operator of Volterra type ,S is an operator of Hamm-merstein type. The global solutions and the unique solutions as well as its iterative approximation are obtained. The results improve and extend many known results of [33-36].