允许Green函数取零值情形下的Neumann问题的正解

Positive solutions of Neumann problem with Green’s function vanishing at some points

本文研究了一类二阶非线性常微分方程Neumann边值问题{y″+a(t)y=λg(t)f(y),t∈[0,1],y′(0)=y′(1)=0,正解的存在性,其中λ是一个正参数,f在∞处是超线性的且f允许变号.此外与这一问题相关的Green函数可以在某些点等于0.主要结果的证明基于Krasnosel’skii不动点定理.

In this paper, we study the existence of positive solutions for a class of second-order nonlinear Neumann problem {y″+a(t)y=λg(t)f(y),t∈[0,1],y′(0)=y′(1)=0,where λ is a positive parameter, f is superlinear at infinity, allowed to change sign, and the Green’s function associated with this problem may vanish at some points. The proof of the main results is based on the Krasnosel’skii fixed-point theorem.