Dynamics of Partial Differential Equations

Volume 8 (2011)

Number 2

Positive solutions to the singular p-Laplacian BVPs with sign-changing nonlinearities and higher-order derivatives in Banach spaces on time scales

Pages: 149 – 171

DOI: http://dx.doi.org/10.4310/DPDE.2011.v8.n2.a5

Authors

Zhaosheng Feng (Department of Mathematics, University of Texas-Pan American, Edinburg, Texas, U.S.A.)

You-Hui Su (School of Mathematics and Physics, Xuzhou University of Technology, Jiangsu, China)

Abstract

In this paper, in order to establish the existence criteria for positive solutions of a multiple-point Dirichlet-Robin BVPs in Banach spaces on time scales, first we prove a fixed point theorem on monotone operators and the Ascoli-Arzela’s theorem on time scales. Then using the monotone operator method, we explore the existence criteria of positive solutions for a general multiple-point Dirichlet-Robin BVPs in Banach spaces on time scales with the singular sign-changing nonlinearities and higher-order derivatives. Finally an example is illustrated to indicate the application of our main results, which generalize some well-known results in the literature.

Keywords

boundary value problem, time scales, fixed point, delta derivative, positive solution, partial ordering, p-Laplacian, Ascoli-Arzela’s Theorem

2010 Mathematics Subject Classification

Primary 34B15, 35B09. Secondary 34A12.

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