Existence of Positive Solutions for Singular Boundary Value Problems with PLaplace Operator 

Author  LiuShuang 
Tutor  SunTao 
School  Northeastern University 
Course  Basic mathematics 
Keywords  Singular Boundary value problem Positive solution Fixed point index Mixed monotone operator 
CLC  O175.8 
Type  Master's thesis 
Year  2010 
Downloads  11 
Quotes  0 
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 pLaplace operator has been attached much attention. In this thesis, we discuss two kinds of higher order singular boundary value problems with pLaplace 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 pLaplace 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 nonnegative 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 pLaplace operator [Φp(u(n1)(t)))’+λf(t,u(t))=0,0＜t1,λ>0, subject to the boundary value conditions where0<η1<η2<…<ηm2<1,αi>0, and f may be singular at t=0, t=1 and u=0.The approach is mixed monotone operator method.