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

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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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References

  1. Li, X., Han, Z., Li, X.: Boundary value problems of fractional \(q\)-difference Schröinger equations. Appl. Math. Lett. 46, 100–105 (2015)

    Article  MathSciNet  Google Scholar 

  2. Wang, G.: Twin iterative positive solutions of fractional \(q\)-difference Schrödinger equations. Appl. Math. Lett. 76, 103–109 (2018)

    Article  MathSciNet  Google Scholar 

  3. Ferreira, R.: Positive solutions for a class of boundary value problems with fractional \(q\)-differences. Comput. Math. Appl. 61, 367–373 (2011)

    Article  MathSciNet  Google Scholar 

  4. 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)

    Article  MathSciNet  Google Scholar 

  5. 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)

    Article  MathSciNet  Google Scholar 

  6. Cui, Y.: Uniqueness of solution for boundary value problems for fractional differential equations. Appl. Math. Lett. 51, 48–54 (2016)

    Article  MathSciNet  Google Scholar 

  7. 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)

    Article  MathSciNet  Google Scholar 

  8. Krasnosel’skii, M.: Positive Solutions of Operator Equations. P. Noordhoff, Groningen (1964)

    MATH  Google Scholar 

  9. Guo, D., Sun, J.: Nonlinear Integral Equations. Shandong Science and Technology Press, Jinan (1987)

    Google Scholar 

  10. Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, New York (1988)

    MATH  Google Scholar 

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Authors and Affiliations

  1. College of Information Science and Engineering, Shandong Agricultural University, Taian, 271018, Shandong, People’s Republic of China

    Kuikui Ma

  2. School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, People’s Republic of China

    Zhenlai Han & Shurong Sun

Authors
  1. Kuikui Ma
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  2. Zhenlai Han
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  3. Shurong Sun
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Correspondence to Kuikui Ma.

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This research is supported by Shandong Provincial Natural Science Foundation (ZR2017MA043).

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Ma, K., Han, Z. & Sun, S. Existence and uniqueness of solutions for fractional q-difference Schrödinger equations. J. Appl. Math. Comput. 62, 611–620 (2020). https://doi.org/10.1007/s12190-019-01299-2

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  • DOI: https://doi.org/10.1007/s12190-019-01299-2

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