双锥不动点定理及其在非线性边值问题中的应用

Fixed Point Theorems in Double Cones and Their Applications to Nonlinear Boundary Value Problems

本文研究了具可变号非线性项的非线性边值问题的正解存在性,推广了 Krasnoselskii 不动点定理,得到了新的锥上不动点定理,并应用这些定理给出这类边值问题正解的存在性．

In order to study the existence of positive solutions to nonlinear boundary value problems（BVPs） with sign-changing nonlinearity, new fixed point theorems in cones are proved at first, which can be regarded as extensions of Krasnoselskii＇s fixed point theorem. Then some new criteria for the existence of positive solutions to BVPs are given by use of these theorems.