IJPAM: Volume 63, No. 1 (2010)

POSITIVE SOLUTIONS TO MULTI-POINT BVPS WITH
$p$-LAPLACIAN ON TIME SCALES

Renhu Wang$^1$, Xiaohong Yuan$^2$
$^{1,2}$Department of Mathematics
Hexi University
Zhangye, Gansu, 734000, P.R. CHINA
$^1$e-mail: wangrh03@lzu.cn


Abstract.Some new and more general sufficient conditions for the existence of at least twin or arbitrary even positive solutions to a multi-point BVPs for $p$-Laplacian dynamic equation on time scales are presented. The methods used in this paper are different from that of the paper by Su and Li (Y.H. Su, W.T. Li, Triple positive solutions of m-point BVPs for p-Laplacian dynamic equations on time scales, Nonlinear Anal., 68 (2008), 1442-1452). Our results generalize and improve some known results. In particular, the results are even new for the special cases of differential and difference equations, as well as in the general time scale setting. As an application, two examples are given to illustrate the results.

Received: July 5, 2010

AMS Subject Classification: 34B15, 39A10

Key Words and Phrases: time scales, boundary value problem, positive solutions, $p$-Laplacian, fixed point theorem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 1