Arbitrary positive solutions to a multi-point p-Laplacian boundary value problem involving the derivative on time scales

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• 作者：You-Hui Su^a ; ^{suyouhui@xzit.edu.cn} ; ^{suyh05@lzu.cn}
• 关键词：Time scales ; Boundary value problem ; Positive solutions ; ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V0V-51V5GK3-5&_mathId=mml8&_user=1489464&_cdi=5656&_pii=S0895717710006503&_rdoc=17&
• 刊名：Mathematical and Computer Modelling
• 出版年：2011
• 出版时间：May 2011
• 年：2011
• 卷：53
• 期：9-10
• 页码：1742-1747
• 全文大小：227 K

文摘

This paper is concerned with the existence of positive solutions to the p-Laplacian dynamic equation subject to boundary conditions , where φ_p(u)=u^p−2u with p>1. By using the fixed-point theorem due to Avery and Peterson, we prove that the boundary value problem has at least triple or arbitrary positive solutions. Our results are new for the special cases of difference equations and differential equations as well as in the general time scale setting. As an application, an example is given to illustrate the result. The interesting point in this paper is that the nonlinear term f is involved with the first-order derivative explicitly.