一类奇异二阶两点边值问题多重正解的局部存在定理

Local Existence Theorems of Multiple Positive Solutions to a Class of Singular Second-Order Two-Point Boundary Value Problems

利用锥拉伸与锥压缩型的Guo-Krasnoselskii不动点定理考察了非线性方程u″(t)+h(t)f(t,u(t)) =0的两点边值问题的正解.f(t,u)是局部本性有界的,只要f(t,u)在某些有界集合上的本性高度是适当的,则该问题可以具有n个正解,其中n是一个任意的正整数。

The positive solutions are considered for a class of two-point boundary value problems of the nonlinear equation u＂（t） ＋ h（t）f（t, u（t）） = 0, by applying the Guo-Kraxnoselskii fixed point theorems of cone expansion-compression type. In this paper, f（t, u） is locallyessentially bounded. The main results show that the problem may have n positive solutions provided the essential heights of f（t, u） are appropriate on some bounded sets, where n is an arbitrary positive integral number.