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Volume 4, Issue 4
Triple Positive Solutions of Boundary Value Problems for High-Order Fractional Differential Equation at Resonance with Singularities

Zhiyuan Liu & Shurong Sun

DOI: 10.12150/jnma.2022.686

J. Nonl. Mod. Anal., 4 (2022), pp. 686-700.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity.

  • Keywords

Triple positive solution, Fractional differential equation, Resonance, Singularity.

  • AMS Subject Headings

34B18, 34A08, 34F15, 35A21

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-686, author = {Liu , Zhiyuan and Sun , Shurong}, title = {Triple Positive Solutions of Boundary Value Problems for High-Order Fractional Differential Equation at Resonance with Singularities}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {4}, number = {4}, pages = {686--700}, abstract = {

In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.686}, url = {http://global-sci.org/intro/article_detail/jnma/21906.html} }
TY - JOUR T1 - Triple Positive Solutions of Boundary Value Problems for High-Order Fractional Differential Equation at Resonance with Singularities AU - Liu , Zhiyuan AU - Sun , Shurong JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 686 EP - 700 PY - 2023 DA - 2023/08 SN - 4 DO - http://doi.org/10.12150/jnma.2022.686 UR - https://global-sci.org/intro/article_detail/jnma/21906.html KW - Triple positive solution, Fractional differential equation, Resonance, Singularity. AB -

In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity.

Zhiyuan Liu & Shurong Sun. (2023). Triple Positive Solutions of Boundary Value Problems for High-Order Fractional Differential Equation at Resonance with Singularities. Journal of Nonlinear Modeling and Analysis. 4 (4). 686-700. doi:10.12150/jnma.2022.686
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