非线性边值问题正解存在性的特征值判据

On the Eigenvalue Criteria for Positive Solutions of Nonlinear Boundary Value Problems

讨论了二阶常微分方程边值问题{-u^n(t)=f(t,u(t)),t∈[0,1],u(0)=u(1)=0正解的存在性,其中f:[0,1]×R^+→R^+连续.给出了该问题存在正解的新特征值判据,该判据改进了以前文献中的相关结果.我们的论证基于锥上的不动点指数理论.

This paper deals with the existence of positive solutions of the second-order boundary value problem {u（0）=u（1）=0 -u″（t）=f（t,u（t））,t∈[0,1],where f：[0,1]×R^＋→R^＋is continuous. We present new eigenvalue criteria for the existence of positive solution to this problem, which improve some existent results. Our discussion is based on the theory of fixed point index in cones.