IJPAM: Volume 59, No. 3 (2010)

EXISTENCE AND NONEXISTENCE OF POSITIVE
SOLUTIONS FOR BVPS ON TIME SCALES

Chen-Huang Hong$^1$, Ching-Yan Lin$^2$
$^{1,2}$General Education Center
National Taipei University of Technology
Taipei, 106, TAIWAN, R.O.C.
$^1$e-mail: hongch@ntut.edu.tw
$^2$e-mail: f10454$@$ntut.edu.tw


Abstract.In this paper we consider the boundary value problem on time scales of the form:

\begin{displaymath}
\left\{
\begin{array}{ll}
(E) &u^{\Delta \Delta}(t)+\lam...
...)=0,
\end{array}
\right.
\end{array}
\right.\leqno{(BVP)}
\end{displaymath}

where $\lambda >0$ is a parameter, $f\in C([0,\sigma(1)]\times [0,\infty),[0,\infty))$. We use a fixed point theorem of Krasnoseskii in a cone to obtain the existence, nonexistence and multiplicity results of positive solutions of the boundary value problem $(BVP)$ for $\lambda$ belonging to a suitable interval.

Received: January 20, 2010

AMS Subject Classification: 34A15

Key Words and Phrases: existence, nonexistence, positive solution, time scales, Green's function, cone, fixed point

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 3