Existence of Positive Solutions for Singular Boundary Value Problems with P-Laplace Operator
|Keywords||Singular Boundary value problem Positive solution Fixed point index Mixed monotone operator|
Boundary value problem for nonlinear ordinary differential equation is a class of very important issue. The research has made great progress and it is still active. Recently, the subject of singular boundary value problem with p-Laplace operator has been attached much attention. In this thesis, we discuss two kinds of higher order singular boundary value problems with p-Laplace operator, and obtain the relevant conclusions of positive solutions.In chapter1, the background of the relevant question is outlined briefly.In chapter2, the author considers the existence of positive solutions for the fourth order four point differential equation with p-Laplace operator (Φp(u"(t)))"=a(t)f(t,u(t),u"(t)),0<t1, subject to the boundary value conditions where a,b,c,d,ξ,η are all non-negative constants,0≤ξ,η≤1,a(t)∈C((0,1),[0,∞)), and a(t) is allowed to be singular at t=0and t=1. The method used is the fixed point index theory.In chapter3, the author concerns with the existence and uniqueness of positive solution for the following n th order m point differential equation with p-Laplace operator [Φp(u(n-1)(t)))’+λf(t,u(t))=0,0＜t1,λ>0, subject to the boundary value conditions where0<η1<η2<…<ηm-2<1,αi>0, and f may be singular at t=0, t=1 and u=0.The approach is mixed monotone operator method.