Existence of positive solutions for singular higher-order differential equations

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• 作者：Lishan Liu ; Xinguang Zhang ; Yonghong Wu
• 关键词：Positive solution ; Singular higher-order eigenvalue problem ; Fixed point theorem ; Positive cone
• 刊名：Nonlinear Analysis
• 出版年：2008
• 出版时间：15 June 2008
• 年：2008
• 卷：68
• 期：12
• 页码：3948-3961
• 全文大小：295 K

文摘

In this paper, we consider the existence of positive solutions for the following singular higher-order eigenvalue problem (HEP):

where λ>0 is a parameter, a(t) may have singularity at ad4f0aad748a7686"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">t=0 and or 1; furthermore, f(t,v₁,v₂,…,v_n) may also be singular at g src=""http://www.sciencedirect.com/cache/MiamiImageURL/B6V0Y-4NKYNT6-4-2/0?wchp=dGLzVlz-zSkWA"" alt=""View the MathML source"" title=""View the MathML source"" align=""absbottom"" border=""0"" height=13 width=""134""/>. Without making any monotone-type assumptions, we establish various lemmas and theorems for the existence of positive solutions of the HEP when d48e51"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">λ is in an explicit interval. In addition, the associated Green function for the above problem is derived.