The Existence Of Positive Solutions Of Several Classes Boundary Value Problems With P Laplace Operator

This paper mainly studies with p Laplace operator boundary value problems, mainlythrough the establishment of operators by using the fixed point theorem, concave operatormethod to take p Laplace operator boundary value problems of differential equation isstudied. This thesis consists of five chapters.The first chapter mainly introduces the boundary value problem of the researchbackground and current situation.The second chapter studies the following with a class p Laplace operator boundaryvalue problemsThe third chapter we get the containing function derivative with p Laplace operatordifferential equations with three point boundary value problem in a certain boundaryproblems for the existence of positive solutions of a necessary and sufficient conditionIn the fourth chapter, we obtained only the existence of only one positive solutioncondition of a two-point boundary value problem by concave operators in certain boundaryconditions . f∈C[0,1]×[0, +∞)â†'[0, +∞)，any u∈C[ 0,1]IR~+，there is any subinterval [a,b](?)[0,1]s.t.f(t,u(t))≠0, f is nondecreasing function,and exists t∈(0,1)u∈(0, +∞),such thatf (t , cu , cv )≥c~λ(p-1)f(t,u,v),(0 < c<1).It has only one positive solution.In the fifth chapter, we obtained only the existence of only one positive solutioncondition of the first order derivative of boundary value problem by concave operators incertain boundary conditions .and based on the fourth chapter, cite specific examples.