Positive solutions of nonresonance semipositone singular Dirichlet boundary value problems

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• 作者：Xinguang Zhang ; Lishan Liu ; Yonghong Wu
• 关键词：Singular boundary value problems ; Semipositone ; Positive solutions ; Nonresonance ; Superlinear ; Sublinear
• 刊名：Nonlinear Analysis
• 出版年：2008
• 出版时间：1 January 2008
• 年：2008
• 卷：68
• 期：1
• 页码：97-108
• 全文大小：232 K

文摘

In the case where the nonlinearity term is allowed to change sign, we study the nonresonance semipositone singular Dirichlet boundary value problem (BVP)

where λ>0 is a parameter, ρ>0 is a constant. We derive an interval of λ such that for any λ lying in this interval, the semipositone BVP has at least one positive solution if f is superlinear or sublinear. The results obtained improve and extend many recent results. Our approach is based on Krasnaselskii’s fixed point theorem in cones.