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october 2013 Nonlinear Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces
Ahmet Yantir, Ireneusz Kubiaczyk, Aneta Sikorska-Nowak
Bull. Belg. Math. Soc. Simon Stevin 20(4): 587-601 (october 2013). DOI: 10.36045/bbms/1382448182

Abstract

This paper is devoted to prove the existence of solutions of the nonlinear Sturm-Liouville boundary value problem on time scales in Banach spaces. We obtain the sufficient conditions for the existence of solutions in terms of Kuratowski measure of noncompactness. Mönch's fixed point theorem is used to prove the main result. By the unification property of time scales, our result is valid for Sturm-Liouville differential equations and difference equations, but more interestingly by the extension property, it is also valid for Sturm-Liouville $q$-difference equation.

Citation

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Ahmet Yantir. Ireneusz Kubiaczyk. Aneta Sikorska-Nowak. "Nonlinear Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces." Bull. Belg. Math. Soc. Simon Stevin 20 (4) 587 - 601, october 2013. https://doi.org/10.36045/bbms/1382448182

Information

Published: october 2013
First available in Project Euclid: 22 October 2013

zbMATH: 1297.34103
MathSciNet: MR3129061
Digital Object Identifier: 10.36045/bbms/1382448182

Subjects:
Primary: 34A40, 34G20, 34N05, 39A13, 46B50

Rights: Copyright © 2013 The Belgian Mathematical Society

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Vol.20 • No. 4 • october 2013
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