Dynamics of Partial Differential Equations

Volume 7 (2010)

Number 1

Positive solutions to P-Laplacian multi-point BVPs on time scales

Pages: 45 – 64

DOI: https://dx.doi.org/10.4310/DPDE.2010.v7.n1.a3

Authors

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

Subei Li (School of Mathematics and Physics, Xuzhou University of Technology, Xuzhou, Jiangsu, China)

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

Abstract

In this paper, we are concerned with the p-Laplacian multi-point boundary value problem with the first-order derivative of the nonlinear term on time scales. Some new sufficient conditions are presented for the existence of at least twin or arbitrary even positive solutions to the multi-point boundary value problem of the p-Laplacian dynamic equation on time scales. In particular, our results are even new for some special cases of differential and difference equations in the general time scale setting. As an application, an example is illustrated at the end of the article.

Keywords

time scales, boundary value problem, positive solutions, p- Laplacian, fixed point theorem

2010 Mathematics Subject Classification

Primary 34B15, 35B09. Secondary 39A10.

Published 1 January 2010