Positive Solutions Of Nonlinear Boundary Value Problems For Two Kinds Of Differential Equations

The study of differential equations is very important in mathematical problems. At the same time, the differential equations also exist in natural science such as physics, biology, automatic model in the light of actual problems, that is to say we build the differential equations.Recently, the existence of positive solutions for nonlinear second-order two-point boundary value problems on half-line has been studied by many authors [1-6]. But most of them are interested in continuous function. Now m-point problems on half-line have been studied in some article. However, the study of singularity is relative few because of the complexity of the equation.In the chapter 1 of this thesis, we explain the present the conditions of the problems. In the chapter 2, we consider the singular equation on half-line. Concerning the first eigenvalue of relevant linear operator and by means of fixed point index theory, the existence of positive solutions is obtained and the example is given.In the chapter3 of this thesis, we consider the three-order and half-positive equation at the basic of [9], we add another function in the equation so that the equation is more universality. The existence of positive solutions is obtained by means of fixed point index theory and the methods similar to those of [10]. The conclusions essentially extend and improve the main results of [9] and the example is given.