The paper deals with the existence of solutions for the dynamic equation on time scales
with the multipoint boundary conditions
where T is a time scale [0, 1] T = {t ∈ T | 0 ≤ t ≤ 1}, a i > 0, i = 1, 2, …, m − 2, b j > 0, j = 1, 2, …, n − 2, 0 < ξ1 < ξ2 < … < ξ m−2 < ρ(1), and 0 < η 1 < η 2 < … < η n−2 < ρ(1). The existence result is given by using Green’s function, the method of upper and lower solutions, and the monotone iterative technique. We also give an example to illustrate our result.
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Published in Neliniini Kolyvannya, Vol. 16, No. 3, pp. 336–349, July–September, 2013.
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Du, Z., Fu, Z. & Kong, L. Existence of Solutions for a Class of Fourth-Order Multipoint Boundary-Value Problems on Time Scales. J Math Sci 201, 310–324 (2014). https://doi.org/10.1007/s10958-014-1991-z
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DOI: https://doi.org/10.1007/s10958-014-1991-z