Some Research On Existence Of Solutions And Explosive Solutions For A Class Of Quasilinear Ordinary Differential Equations

In this paper, we study the existence of solutions and explosive solutions for a class of quasilinear ordinary differential equations with nonlinear boundary conditions, these problems basing on the study of the p-Laplace equation, generalized reaction-diffusion theory, non-Newtonian fluid theory, and the turbulent flow of a gas in porous medium.The main contents are as follows.In chapter 1, we introduce the main problems that we study.In chapter 2, firstly, by using the method of upper and lower solutions, we study the existence of solutions for a class of the second order quasilinear integrodifferen-tial equations with nonlinear boundary conditions; secondly, using the results of the existence of solutions for a class of the second order quasilinear integrodifferential equations with nonlinear boundary conditions, we are concerned with the third and fourth order quasilinear ordinary differential equations with the nonlinear boundary conditions, the corresponding results of the semilinear high order ordinary differential equations with nonlinear boundary conditions become general.In chapter 3, by the quadrature method, we show that there exists an explosive solution for a class of quasilinear ordinary differential equations with boundary conditions.