• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.65-71
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• 2019

This paper is concerned with the existence of positive solutions of the nonlinear Neumann boundary value problems $$\{u^{{\prime}{\prime}}+a(t)u={\lambda}b(t)f(u),\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$, where $a,b{\in}C[0,1]$ with $a(t)>0,\;b(t){\geq}0$ and the Green's function of the linear problem $$\{u^{{\prime}{\prime}}+a(t)u=0,\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$ may change its sign on $[0,1]{\times}[0,1]$. Our analysis relies on the Leray-Schauder fixed point theorem.