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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 1-2/2020

29-10-2019 | Original Research

Existence and uniqueness of solutions for fractional q-difference Schrödinger equations

Authors: Kuikui Ma, Zhenlai Han, Shurong Sun

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2020

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Abstract

The aim of this paper is to investigate the existence and uniqueness of solutions for a class of fractional q-difference Schrödinger equations appeared in Li et al. (Appl Math Lett 46:100–105, 2015). By use of two completely different approaches—\(u_0\)-positive operator and monotone iterative technique, this paper not only establishes excellent conditions to ensure the existence and uniqueness of solutions for this problem, but also constructs iterative sequences to approximate the solution. As applications, examples are presented to illustrate our main results.
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Literature
1.
Li, X., Han, Z., Li, X.: Boundary value problems of fractional \(q\)-difference Schröinger equations. Appl. Math. Lett. 46, 100–105 (2015)MathSciNetCrossRef
2.
Wang, G.: Twin iterative positive solutions of fractional \(q\)-difference Schrödinger equations. Appl. Math. Lett. 76, 103–109 (2018)MathSciNetCrossRef
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Ferreira, R.: Positive solutions for a class of boundary value problems with fractional \(q\)-differences. Comput. Math. Appl. 61, 367–373 (2011)MathSciNetCrossRef
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Li, X., Han, Z., Sun, S., et al.: Eigenvalue problems of fractional \(q\)-difference equations with generalized \(p\)-Laplacian. Appl. Math. Lett. 57, 46–53 (2016)MathSciNetCrossRef
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Liang, S., Zhang, J.: Existence and uniqueness of positive solutions for three-point boundary value problem with fractional \(q\)-differences. J. Appl. Math. Comput. 40, 277–288 (2012)MathSciNetCrossRef
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Cui, Y.: Uniqueness of solution for boundary value problems for fractional differential equations. Appl. Math. Lett. 51, 48–54 (2016)MathSciNetCrossRef
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Zhai, C., Ren, J.: Positive and negative solutions of a boundary value problem for a fractional \(q\)-difference equation. Adv. Differ. Equ. 2017, 82 (2017)MathSciNetCrossRef
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Krasnosel’skii, M.: Positive Solutions of Operator Equations. P. Noordhoff, Groningen (1964)MATH
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Guo, D., Sun, J.: Nonlinear Integral Equations. Shandong Science and Technology Press, Jinan (1987)
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Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, New York (1988)MATH
Metadata
Title
Existence and uniqueness of solutions for fractional q-difference Schrödinger equations
Authors
Kuikui Ma
Zhenlai Han
Shurong Sun
Publication date
29-10-2019
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 1-2/2020
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-019-01299-2

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