Solutions Of Singular Boundary Value Problems For One Dimensional Third-order P-Laplacian Equation

In this paper, we mainly discussed the existence of the positive solutions for the following nonlinear third-order p-Laplacian singular boundary value problems Where φp(s)=|s|(p-2)s, b(t) is singular at t= 0 or t= 1, g(t, y) is also singular at y= 0. By using fixed point index theorem, fixed point theorem, comparison theorem and interrelated inequation, the sufficient conditions for the existence of at least one positive solutions,at least two positive solutions, at least three positive solutions and infinitely many positive solutions are established.In chapter one, the research background, significance, status and summary of the paper are introduced.In chapter two, we present the preliminaries and the related lemmas and theorems.In chapter three, by using fixed point index theorem, comparison theorem and inter-related inequation, we established the sufficient condition for the existence of at least one positive solution to the nonlinear boundary value problem.In chapter four, we prove the sufficient condition for the existence of at least one positive solution to the nonlinear boundary value problem by using the fixed point theorem.In chapter five, we use Leggett-William theorem to discuss the existence of triple positive solutions for the nonlinear singular boundary value problem.In chapter six, by applying fixed point index theorem, we study the existence of infinitely many positive solutions for the nonlinear singular boundary value problem.In chapter seven, we give some examples to illuminate the effectiveness of the theo-rems.