一般Lidstone边值问题的n个正解的存在性

考察了含所有偶数阶导数的一般Lidstone边值问题的正解和对称正解.通过 选择合适的Banach空间和锥,对该问题建立了n个正解或者对称正解的存在性,其 中n是一个任意的自然数.基本工具是等价范数和锥拉伸与锥压缩型的Krasnosel'skii 不动点定理. 结论的主要条件是局部的.换言之,如果非线性项f在某些有界集上的 "高度"是适当的,则该问题可以具有n个正解.

Existence of n Positive Solutions to General Lidstone Boundary Value Problems

The positive solutions and symmetric positive solutions of the general Lidstone boundary value problem with all even-order derivatives are considered. By choosing suitable Banach space and cone, the existence of n positive solutions or symmetric positive solutions is established for the problem, where n is an arbitrary natural number. The basic tools used are equivalent norm and Krasnosel'skii fixed point theorem of cone expansion-compression type. The main conditions of the results are local. In other words, the problem may possess n positive solutions provided the "height" of the nonlinear term f on some bounded sets are appropriate.