Positive solutions for fractional differential equation at resonance under integral boundary conditions

• Autorzy: Wang, Youyu , Huang, Yue , Li, Xianfei
• Języki publikacji: EN

Abstrakty

EN

By using the theory of fixed point index and spectral theory of linear operators, we study the existence of positive solutions for Riemann-Liouville fractional differential equations at resonance. Our approach will provide some new ideas for the study of this kind of problem.

Słowa kluczowe

PL

ułamkowe równanie różniczkowe; rozwiązanie dodatnie; rezonans; punkt stały; funkcja Greena

EN

fractional differential equation; positive solution; resonance; fixed point index; Green’s function

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 238--253
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Wang, Youyu

• Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, P. R. China,

autor

Huang, Yue

• Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, P. R. China,

autor

Li, Xianfei

• Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, P. R. China,

Bibliografia

• [1] T. Chen, W. Liu, and Z. Hu, A boundary value problem for fractional differential equation with p-Laplacian operator at resonance, Nonlinear Anal. 75 (2012), 3210–3217.
• [2] W. Jiang, The existence of solutions to boundary value problems of fractional differential equations at resonance, Nonlinear Anal. 74 (2011), 1987–1994.
• [3] F. Wang, Y. Cui, and F. Zhang, Existence of nonnegative solutions for second order m-point boundary value problems at resonance, Appl. Math. Comput. 217 (2011), 4849–4855.
• [4] Z. Bai, Solvability for a class of fractional m-point boundary value problem at resonance, Comput. Math. Appl. 62 (2011), 1292–1302.
• [5] Y. Ji, W. Jiang, and J. Qiu, Solvability of fractional differential equations with integral boundary conditions at resonance, Topol. Method. Nonl. Anal. 42 (2013), 461–479.
• [6] W. Jiang, Solvability of fractional differential equations with p-Laplacian at resonance, Appl. Math. Comput. 260 (2015), 48–56.
• [7] Y. Wu and W. Liu, Positive solutions for a class of fractional differential equations at resonance, Adv. Differ. Equ. 2015 (2015), 241.
• [8] T. Chen, W. Liu, and H. Zhang, Some existence results on boundary value problems for fractional p-Laplacian equation at resonance, Bound. Value Probl. 2016 (2016), 51.
• [9] W. Zhang and W. Liu, Existence of solutions for fractional differential equations with infinite point boundary conditions at resonance, Bound. Value Probl. 2018 (2018), 36.
• [10] Y. Wang and H. Wang, Triple positive solutions for fractional differential equation boundary value problems at resonance, Appl. Math. Lett. 106 (2020), 106376.
• [11] Y. D. Ri, H. C. Choi, and K. J. Chang, Constructive existence of solutions of multi-point boundary value problem for Hilfer fractional differential equation at resonance, Mediterr. J. Math. 17 (2020), 95.
• [12] Y. Wang and L. Liu, Positive solutions for a class of fractional 3-point boundary value problems at resonance, Adv. Differ. Equ. 2017 (2017), 7.
• [13] Y. Wang, Necessary conditions for the existence of positive solutions to fractional boundary value problems at resonance, Appl. Math. Lett. 97 (2019), 34–40.
• [14] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier, Amsterdam, The Netherlands, 2006.
• [15] X. Meng and M. Stynes, The Green function and a maximum principle for a Caputo two-point boundary value problem with a convection term, J. Math. Anal. Appl. 461 (2018), no. 1, 198–218.
• [16] Y. Wang, X. Li, and Y. Huang, The Green’s function for Caputo fractional boundary value problem with a convection term, AIMS Math. 7 (2022), no. 4, 4887–4897, DOI: https://doi.org/10.3934/math.2022272.
• [17] D. Guo and J. Sun, Nonlinear Integral Equations, Shandong Science and Technology Press, Jinan, 1987 (in Chinese).
• [18] D. Guo, Nonlinear Functional Analysis, Shandong Science and Technology Press, Jinan, 1985 (in Chinese).

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).

Identyfikatory

DOI

10.1515/dema-2022-0026