一类奇异非线性边界值问题正解的存在性和非唯一性

Existence and Nonuniqueness of Positve Solutions to a Class of Singular Nonlinear Boundary Value Problems

本文研究了一类奇异非线性边界值问题ｇｐ（ｘ）ｇ″（ｘ）＋ｈ（ｘ）＝０，－ｋ＜ｘ＜１，ｇ′（－ｋ）＝Ｃ，ｇ（１）＝０，ｋ＞０正解的存在性和非唯一性．问题起源于幂律流体理论中著名的边界层方程．ｕｕｘ＋ｖｕｙ＝ｙ（γ｜ｕｙ｜ｎ－１ｕｙ），ｕｘ＋ｖｙ＝０，ｕ｜ｙ＝０＝－Ｕｗ，ｖ｜ｙ＝０＝Ｖｗ（ｘ），ｕ｜ｙ＝＋∞＝Ｕ∞．

This paper studies the existence and nonuniqueness of positive solutions for a class of singular nonlinear boundary value problems g p(x)g ″(x)+h(x)=0,-k<x<1,g′(-k)=C,g(1)=0,k>0 which originates from the famous boundary layer equation in the theory of power law fluids. uux+vuy=y( γ|uy| n-1 uy),ux+vy=0,u| y=0 =-U w,v| y=0 =V w(x),u| y=+∞ =U ∞.