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Zbl 1170.34309
Karaca, Ilkay Yaslan
Fourth-order four-point boundary value problem on time scales. (English)
[J] Appl. Math. Lett. 21, No. 10, 1057-1063 (2008). ISSN 0893-9659

This paper studies the existence of solutions for a fourth order four-point boundary value problem on time scales. The results are obtained by an application of the Leray--Schauder fixed point theorem. This work is motivated by the continuous time results in [{\it S. Chen, Wei Ni, C. Wang}, Appl. Math. Lett. 19, No.~2, 161--168 (2006; Zbl 1096.34009)] for ordinary differential equations, and by the methods from [{\it J.-P. Sun}, Nonlinear Anal., Theory Methods Appl. 64, No.~3 (A), 629--636 (2006; Zbl 1099.34022)] for the third order problems on time scales.
[Roman Šimon Hilscher (Brno)]

MSC 2000:: *34B10 Multipoint boundary value problems
39A10 Difference equations
47N20 Appl. of operator theory to differential and integral equations

Keywords: Positive solution; Fixed point theorem; Time scale; Dynamic equation; Cone

Citations: Zbl 1096.34009; Zbl 1099.34022

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