The Existence Of Positive Solutions For Boundary Value Problems For Two Calss Of Differential Equation Systems With The Frist Order Derivative

Differential equations arise from the development of production practice and scientific technology, and have a profound actual background, as modern science and technology the indispensable tool for solving problems. In the fields of economic, biological species, astronomy, and physics, differential equations has it extremely important application value. Differentia equations are presented played a significant results for solving the problem. During the development of the problem, the differential equations have provided an extremely appropriate mathematical mode, trigger a new field.It's very important to research on the existence of positive solutions of boundary value problems for differential equations. Firster, we make clear whether and how many solutions exist, by means of the methods of nonlinear functional analysis arises recent decades years, has greatly attracted many mathematics workers' attention.This dissertation discusses the existence of positive solutions for boundary value problems for a class of differential equtions system with the first order derivative.Firstly, we study the existence of positive solutions for some p-Laplacian boundary value problems with dependence on the second order quasilinear multi-point boundary value problems, by using a new fixed point theorem in cone to obtain the existence:of at least one positive solution.Secondly, we discuss the existence of at least one positive solutions for second order differential equtions m-point boundary value problems with dependence on the first order derivative.Thirdly, through the fixed point theorem which is proved by measure theory, we obtain pseudo-symmetric solutions for differential equtions three-point boundary value problems with dependence on the first order derivative.Finally, by contructing pseudo-symmetric operator, we change the problem of finding the solution for ordinary differential equations into the problem of finding out the fixed point of the operator, we obtain pseudo-symmetric solutions for differential equtions three-point p-Laplacian boundary value problems.