IJPAM: Volume 52, No. 5 (2009)
POSITIVE SOLUTIONS FOR STURM-LIOUVILLE
BOUNDARY VALUE PROBLEMS ON A MEASURE CHAIN
BOUNDARY VALUE PROBLEMS ON A MEASURE CHAIN
Sheng-Quan Liang
, Jian-Ping Sun
Gansu Polytechnic College of
Animal Husbandry and Engineering
Huangyang Town, Wuwei, Gansu, 733006, P.R. CHINA
Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, Gansu, 730050, P.R. CHINA
e-mail: [email protected]



Animal Husbandry and Engineering
Huangyang Town, Wuwei, Gansu, 733006, P.R. CHINA

Lanzhou University of Technology
Lanzhou, Gansu, 730050, P.R. CHINA
e-mail: [email protected]
Abstract.In this paper we consider the following differential equation on a measure chain
![\begin{displaymath}
u^{\Delta \Delta }(t)+f(t,u(\sigma (t)))=0,t\in [a,b],
\end{displaymath}](img3.png)
satisfying Sturm-Liouville boundary value condition

Some results of the existence and multiplicity are obtained by using Krasnoselskii's Fixed Point Theorem in a cone. In particular, it is proved that the above boundary value problem has


Received: February 27, 2008
AMS Subject Classification: 34B15, 39A10
Key Words and Phrases: measure chain, positive solution, cone, fixed point
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 5