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 |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:asx&genre=article&issn=00442267&ISBN=&volume=106&issue=6&date=20260601&spage=1&pages=1-18&title=ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik&atitle=Multiplicity%20Results%20for%20a%20Fractional%20p%E2%80%90Laplacian%20Equation%C2%A0Involving%20Homogeneous%20Nonlinearities%20With%20Subcritical%20or%20Critical%20Growth.&aulast=Akrout%2C%20Kamel&id=DOI:10.1002/zamm.70483 Name: Full Text Finder (for New FTF UI) (ns324271) Category: fullText Text: Full Text Finder MouseOverText: Full Text Finder |
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| Items | – Name: Title Label: Title Group: Ti Data: Multiplicity Results for a Fractional p‐Laplacian Equation Involving Homogeneous Nonlinearities With Subcritical or Critical Growth. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Akrout%2C+Kamel%22">Akrout, Kamel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Fareh%2C+Souraya%22">Fareh, Souraya</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ghanmi%2C+Abdeljabbar%22">Ghanmi, Abdeljabbar</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> abdeljabbar.ghanmi@lamsin.rnu.tn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22ZAMM+--+Journal+of+Applied+Mathematics+%26+Mechanics+%2F+Zeitschrift+für+Angewandte+Mathematik+und+Mechanik%22">ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik</searchLink>. Jun2026, Vol. 106 Issue 6, p1-18. 18p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Nonlinear+operators%22">Nonlinear operators</searchLink><br />*<searchLink fieldCode="DE" term="%22Differential+operators%22">Differential operators</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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<m<r<p<q≤ps*=NpN−sp$0<m<r<p<q\le p_{s}^{\ast }=\frac{Np}{N-sp}$. Our results are novel and extend previous works by considering more general growth conditions. [ABSTRACT FROM AUTHOR] |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/zamm.70483 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 1 Subjects: – SubjectFull: Nonlinear operators Type: general – SubjectFull: Differential operators Type: general Titles: – TitleFull: Multiplicity Results for a Fractional p‐Laplacian Equation Involving Homogeneous Nonlinearities With Subcritical or Critical Growth. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Akrout, Kamel – PersonEntity: Name: NameFull: Fareh, Souraya – PersonEntity: Name: NameFull: Ghanmi, Abdeljabbar IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00442267 Numbering: – Type: volume Value: 106 – Type: issue Value: 6 Titles: – TitleFull: ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Type: main |
| ResultId | 1 |