一般Lidstone边值问题的解的存在性

考察了含有各阶导数的一般Lidstone边值问题的存在性. 利用Leray-Schauder不动点定理、等价范数及积分方程组技巧证明了解或正解的两个存在定理. 这些定理在应用上非常方便. 换句话说, 通过考察非线性项在某个有界子集上的“高度”就能决定解的存在性.

Existence of Solution for General Lidstone Boundary Value Problems

The existence of general Lidstone boundary value problems with all order derivatives is considered. By making use of Leray-Schauder fixed point theorem, equivalent norm and the techniques of system on integral equations, two existence theorems of solutions and positive solutions are proved.These theorems are very convenient for the applications. In other words, the existence can be determined by considering the "height" of nonlinear term on a bounded set.