With P-laplace Operator Differential Equations, Two Point Boundary Value Problem

The BVPs with p－Laplace arise in a variety of applied areas such as applied mechanics,astrophysics and nonlinear partial differential equations. The paper studies the boundaryvalue problems for ordinary differential equation with p－Laplace operator by using fixedpoint theorems and upper and lower solutions and monotone iterative. Firstly, we get thesufficient condition of sevaral positive solutions and the necessary and sufficient conditionsof positive solution for the BVPs with p－Laplace of nonlinear term with the first orderderivative of unknown function. In addition, it is a innovation that we set up the way ofmonotone iterative technique for its approximate solutions.In this paper, we study three respects. In the first part, we study the sufficient conditionof positive solution to the BVPs with p－Laplace . In the second part, we obtain thenecessary and sufficient condition of positive solution to the BVPs with p－Laplace . In thethird part, we get its approximate positive solutions by using monotone iterative technique.The paper consists of five chapters:In chapter 1, we mainly introduce the background and the progress of the two pointBVPs with p－Laplace . In addition, we also present the organized of this paper.In chapter 2, we get three positive solutions of (φ_p(u'(t))) + q(t)f(t,u(t),u'(t)) =0, (0 < t < 1) with u(0) - g₁(u'(0)) = 0, u(1) + g₂(u'(1)) = 0 , by using the fixed pointtheorem.In chapter 3, we get infinite positive solutions of (φ_p(u'(t)))' + q(t)f(t,u(t),u (t)) =0, (0 < t < 1) with u(0) - g₁(u'(0)) = 0, u(1) + g₂(u'(1)) = 0 , by using the tensile andcompression cone fixed point theorem. a(t) has infinite Singular points in (0, 1/2) .In chapter 4, we get the necessary and su?cient condition of positive solution to theBVPs with p－Laplace (φ_p(u'(t)))' + q(t)f(t,u(t),u'(t)) = 0, (0 < t < 1) with u(0) =u(1) = c , by using the method of upper and lower solutions.In chapter 5, we get the existence condition of positive solution to the BVPs withp－Laplace (φ_p(u'(t)))' + q(t)f(t,u(t),u (t)) = 0, (0 < t < 1) with u(0) - g₁(u'(0)) = 0, u(1) + g₂(u'(1)) = 0 , and we set up the way of monotone iterative technique for itsapproximate positive solutions.