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Nonlocal eigenvalue problems with indefinite weight


In the present paper, we consider a class of eigenvalue problems driven by a nonlocal integro-differential operator $\mathcal{L}_{K}^{p(x)}$ with Dirichlet boundary conditions. Under certain assumptions on p and q, we establish that any $\lambda>0$ suficiently small is an eigenvalue of the nonhomogeneous nonlocal problem ($\mathcal{P}_{\lambda}$).

Розглядається клас спектральних задач, пов'язаних із нелокальним інтегро-диференціальним оператором $\mathcal{L}_{K}^{p(x)}$ із крайовою умовою Дирихле. За певних припущень щодо $p$ і $q$ доведено, що кожне достаньо мале $\lambda>0$ є власним значенням неоднорідної нелокальної задачі ($\mathcal{P}_{\lambda}$).

Key words: Fractional $p(x, y)-$Laplacian problems, eigenvalue problem, Ekeland's variational principle, indefinite weight, fractional Sobolev space.

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Article Information

TitleNonlocal eigenvalue problems with indefinite weight
SourceMethods Funct. Anal. Topology, Vol. 26 (2020), no. 3, 283-294
MilestonesReceived 12/05/2020; Revised 27/08/2020
CopyrightThe Author(s) 2020 (CC BY-SA)

Authors Information

Said Taarabti
Laboratory of Systems Engineering and Information Technologies (LISTI), National School of Applied Sciences of Agadir, Ibn Zohr University, Morocco.

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Said Taarabti, Nonlocal eigenvalue problems with indefinite weight, Methods Funct. Anal. Topology 26 (2020), no. 3, 283-294.


@article {MFAT1400,
    AUTHOR = {Said Taarabti},
     TITLE = {Nonlocal eigenvalue problems with indefinite weight},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {26},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {283-294},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_3.2020.09},
       URL = {},


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