Existence of solutions of Dirichlet problems for one dimensional fractional equations

Armin Hadjian; Juan J. Nieto; Armin Hadjian; Juan J. Nieto

doi:10.3934/math.2022336

AIMS Mathematics

2022, Volume 7, Issue 4: 6034-6049. doi: 10.3934/math.2022336

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Research article

Existence of solutions of Dirichlet problems for one dimensional fractional equations

Armin Hadjian ^{1
,
,},
Juan J. Nieto ²

1.
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran
2.
CITMAga, Institute of Mathematics, University of Santiago de Compostela, Santiago de Compostela 15782, Spain

Received: 07 September 2021 Revised: 13 December 2021 Accepted: 29 December 2021 Published: 17 January 2022
MSC : 34A08, 35A15, 26A33

We establish the existence of infinitely many solutions for some nonlinear fractional differential equations under suitable oscillating behaviour of the nonlinear term. These problems have a variational structure and we prove our main results by using a critical point theorem due to Ricceri.
- fractional differential equations,
- Caputo fractional derivatives,
- infinitely many solutions,
- variational methods
Citation: Armin Hadjian, Juan J. Nieto. Existence of solutions of Dirichlet problems for one dimensional fractional equations[J]. AIMS Mathematics, 2022, 7(4): 6034-6049. doi: 10.3934/math.2022336

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Abstract

We establish the existence of infinitely many solutions for some nonlinear fractional differential equations under suitable oscillating behaviour of the nonlinear term. These problems have a variational structure and we prove our main results by using a critical point theorem due to Ricceri.

References

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