Abstract
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.
Full Text
Article Information
| Title | Nonlocal eigenvalue problems with indefinite weight |
| Source | Methods Funct. Anal. Topology, Vol. 26 (2020), no. 3, 283-294 |
| DOI | 10.31392/MFAT-npu26_3.2020.09 |
| MathSciNet |
MR4165159 |
| Milestones | Received 12/05/2020; Revised 27/08/2020 |
| Copyright | The 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.
Citation Example
Said Taarabti, Nonlocal eigenvalue problems with indefinite weight, Methods Funct. Anal. Topology 26
(2020), no. 3, 283-294.
BibTex
@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},
MRNUMBER = {MR4165159},
DOI = {10.31392/MFAT-npu26_3.2020.09},
URL = {http://mfat.imath.kiev.ua/article/?id=1400},
}
