一类奇异非线性两点边值问题

A Class of Singular Nonlinear Two-point Boundary Value Problems

在本文中,我们研究奇异非线性两点边值问题 y^n(t)+f(t,y(t))=0,0≤k<t<1, y′(k)=c,y(1)=0的正解的存在唯一性.这里c实数,函数f(t,y)在[k,1]×(0,∞)上非负连续,且关于y单调不增.

The present paper deals with the singular nonlinear two-point boundary value problem y'(t) +∫(t,y) = 0, 0≤k<t<1, y'(k)=c, y(l) = 0 with a view to obtaining the uniqueness and existence of positive solutions. Here, c is a real number, and the function ∫ is assumed to be decreasing on the second variable, with the singularity modeled in the special case of ∫(t,y)=ty-p, p>0.