On a nonlocal problem involving the generalized anisotropic (·)-Laplace operator

Mustafa Avci

On a nonlocal problem involving the generalized anisotropic (·)-Laplace operator

Mustafa Avci

Centre for Science

Research output: Contribution to journal › Journal Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we study an anisotropic nonlocal problem which is a stationary counterpart of the Kirchhoff equation settled in the variable exponent Sobolev spaces. By using the variational approach and applying the Mountain-Pass theorem along with the Fountain theorem, we obtain the existence and multiplicity of nontrivial weak solutions.

Original language	English
Pages (from-to)	259-272
Number of pages	14
Journal	Annals of the University of Craiova, Mathematics and Computer Science Series
Volume	43
Issue number	2
Publication status	Published - 2016

Keywords

(·)-Laplace operator
Anisotropic variable exponent Sobolev spaces
Fountain theorem
Leray-Lions type operator
Mountain-Pass theorem
Nonlocal problem
Variational approach

Cite this

@article{855ab932f94c4cb8b83de2e1ecab77a8,

title = "On a nonlocal problem involving the generalized anisotropic (·)-Laplace operator",

abstract = "In this paper, we study an anisotropic nonlocal problem which is a stationary counterpart of the Kirchhoff equation settled in the variable exponent Sobolev spaces. By using the variational approach and applying the Mountain-Pass theorem along with the Fountain theorem, we obtain the existence and multiplicity of nontrivial weak solutions.",

keywords = "(·)-Laplace operator, Anisotropic variable exponent Sobolev spaces, Fountain theorem, Leray-Lions type operator, Mountain-Pass theorem, Nonlocal problem, Variational approach",

author = "Mustafa Avci",

year = "2016",

language = "English",

volume = "43",

pages = "259--272",

number = "2",

}

TY - JOUR

T1 - On a nonlocal problem involving the generalized anisotropic (·)-Laplace operator

AU - Avci, Mustafa

PY - 2016

Y1 - 2016

N2 - In this paper, we study an anisotropic nonlocal problem which is a stationary counterpart of the Kirchhoff equation settled in the variable exponent Sobolev spaces. By using the variational approach and applying the Mountain-Pass theorem along with the Fountain theorem, we obtain the existence and multiplicity of nontrivial weak solutions.

AB - In this paper, we study an anisotropic nonlocal problem which is a stationary counterpart of the Kirchhoff equation settled in the variable exponent Sobolev spaces. By using the variational approach and applying the Mountain-Pass theorem along with the Fountain theorem, we obtain the existence and multiplicity of nontrivial weak solutions.

KW - (·)-Laplace operator

KW - Anisotropic variable exponent Sobolev spaces

KW - Fountain theorem

KW - Leray-Lions type operator

KW - Mountain-Pass theorem

KW - Nonlocal problem

KW - Variational approach

UR - http://www.scopus.com/inward/record.url?scp=85011536629&partnerID=8YFLogxK

M3 - Journal Article

AN - SCOPUS:85011536629

SN - 1223-6934

VL - 43

SP - 259

EP - 272

JO - Annals of the University of Craiova, Mathematics and Computer Science Series

JF - Annals of the University of Craiova, Mathematics and Computer Science Series

IS - 2

ER -

On a nonlocal problem involving the generalized anisotropic (·)-Laplace operator

Abstract

Keywords

Other files and links

Fingerprint

Cite this