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The Nehari Manifold for a Class of Singular $\psi$-Riemann-Liouville Fractional with $p$-Laplacian Operator Differential Equations
Samah Horrigue, Mona Alsulami and Bayan Abduallah Alsaeedi

Adv. Appl. Math. Mech. DOI: 10.4208/aamm.OA-2022-0009

Publication Date : 2024-06-21

  • Abstract

Using Nehari manifold method  combined with fibring maps, we show the existence of nontrivial, weak, positive solutions of the nonlinear $\psi$-Riemann-Liouville fractional boundary value problem involving the $p$-Laplacian operator, given by

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where $\lambda>0$, $0 < \gamma <1<p$ and $\frac{1}{p} < \alpha \leq1, $, $g \in C([0,T])$ and $f \in C^{1}([0,T]\times \mathbb{R,\mathbb{R}})$. A useful examples are presented in order to illustrate the validity of our main results.


  • Copyright

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