一类非线性奇异边值问题多重正解的存在性

摘要: 讨论微分方程(φ(y′))′+g(t)f(t,y)=0在非线性边 值条件y(0)-B0(y′(0))=y(1)+B1(y′(1))=0下的多重正解存在性问题. 其中, g可 允许在t=0和t=1时有奇性. 利用Leggett-Williams不动点定理， 证明方程有3个正解. 进一步应用该不动点定理， 可得到更多甚至无穷多个正解.

Existence of multiple positive solutions for a class of nonlinear singular boundary value problems

The existence of multiple positive solutions of differe ntial equation (φ(y′))′+g(t)f(t,y)=0 under nonlinear boundary value condi tion y(0)-B₀(y′(0))=y(1)+B1(y′(1))=0 is studied, where g is allowed to be singular at the end points of (0,1). The authors prove with the use of L eggett-Williams fixed-point theorem that the problem has at least three positi ve solutions. By further using the theorem, they show that more, even infinitely many positive solutions may be obtained.