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Fourth-order four-point boundary value problem on time scales. (English) Zbl 1170.34309

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 [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 [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.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
39A10 Additive difference equations
47N20 Applications of operator theory to differential and integral equations
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References:

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