Bulletin of the Belgian Mathematical Society - Simon Stevin

Nonlinear Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces

Ahmet Yantir, Ireneusz Kubiaczyk, and Aneta Sikorska-Nowak

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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.

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Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 4 (2013), 587-601.

First available in Project Euclid: 22 October 2013

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Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 34A40: Differential inequalities [See also 26D20] 34N05: Dynamic equations on time scales or measure chains {For real analysis on time scales or measure chains, see 26E70} 39A13: Difference equations, scaling ($q$-differences) [See also 33Dxx] 46B50: Compactness in Banach (or normed) spaces

Sturm-Liouville problem Banach space measure of noncompactness time scale


Yantir, Ahmet; Kubiaczyk, Ireneusz; Sikorska-Nowak, Aneta. Nonlinear Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 4, 587--601. doi:10.36045/bbms/1382448182. https://projecteuclid.org/euclid.bbms/1382448182

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