Academic Journal
Multiplicity Results for a Fractional p‐Laplacian Equation Involving Homogeneous Nonlinearities With Subcritical or Critical Growth.
| Τίτλος: | Multiplicity Results for a Fractional p‐Laplacian Equation Involving Homogeneous Nonlinearities With Subcritical or Critical Growth. |
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| Συγγραφείς: | Akrout, Kamel1 (AUTHOR), Fareh, Souraya2 (AUTHOR), Ghanmi, Abdeljabbar3 (AUTHOR) abdeljabbar.ghanmi@lamsin.rnu.tn |
| Πηγή: | ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. Jun2026, Vol. 106 Issue 6, p1-18. 18p. |
| Θεματικοί όροι: | *Nonlinear operators, *Differential operators |
| Περίληψη: | In this article, we investigate certain subcritical and critical equations involving the fractional p$p$‐Laplace operator. More precisely, using fibering maps and the Nehari manifold, we establish the multiplicity of solutions for the following problem: (−Δ)psu(x)=uq−2u+μk(x,u)+λl(x,u),u>0inΩ,u=0onRN∖Ω,$$\begin{equation*} \left\lbrace \def\eqcellsep{&}\begin{array}{l}\mathbf{(-}\Delta \mathbf {)}_{p}^{s}u(x)={\left|u\right|}^{q-2}u+\mu k(x,u)+\lambda l(x,u),\;u>0\text{ in }\Omega, \\ \\ u=0\text{ on}\, \mathbb {R}^{N}\setminus \Omega, \end{array} \right. \end{equation*}$$where Ω⊂RN$\Omega \subset \mathbb {R}^{N}$ is a smooth bounded domain, (−Δ)psu$\mathbf {(- }\Delta \mathbf {)}_{p}^{s}u$ is the fractional p$p$‐Laplacian, N>ps,s∈(0,1),ρ$N>ps,s\in (0,1),\rho$ and σ$\sigma$ are positive parameters, k$k$ and l$l$ are homogeneous functions of degrees r−1$\left(r-1\right)$ and m−1$\left(m-1\right)$ with 0 |
| Βάση Δεδομένων: | Academic Search Index |
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