ON RESONANT FRACTIONAL <i>Q</i>-DIFFERENCE SCHRÖDINGER EQUATIONS

Zhiyuan Liu; Zhenlai Han

doi:10.11948/20220385

2023 Volume 13 Issue 5

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Zhiyuan Liu, Zhenlai Han. ON RESONANT FRACTIONAL Q-DIFFERENCE SCHRÖDINGER EQUATIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2487-2503. doi: 10.11948/20220385

Citation:

Zhiyuan Liu, Zhenlai Han. ON RESONANT FRACTIONAL Q-DIFFERENCE SCHRÖDINGER EQUATIONS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2487-2503. doi: 10.11948/20220385

ON RESONANT FRACTIONAL Q-DIFFERENCE SCHRÖDINGER EQUATIONS

Zhiyuan Liu^1,,
Zhenlai Han^1, ,

1.
School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China

Author Bio: Email: liuzhiyuan2273@163.com(Z. Liu)
Corresponding author: Email: hanzhenlai@163.com(Z. Han)

Abstract

Abstract

The research of fractional $ q $-difference Schrödinger equations has attracted the attention of scholars and abundant results have been obtained in recent years. However, as far as we know, there are no results on resonant fractional $ q $-difference Schrödinger equations. In this paper, we investigate the boundary value problems for fractional $ q $-difference Schrödinger equations at resonance. By virtue of fixed point index theorem and spectral theory of linear operators, we obtain the multiplicity of positive solutions. In addition, we get different stability results, including Ulam-Hyres stability and generalized Ulam-Hyres stability. Give relevant examples to prove the main results.
- Fractional q-difference Schrödinger equations /
- Resonance /
- boundary value problems /
- positive solutions /
- fixed point index
MSC: 26A33, 34F15, 39A27, 34B18, 37C25

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References

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