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Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) Condition

Authors :
Weichun Bu
Tianqing An
Guoju Ye
Said Taarabti
Source :
Journal of Function Spaces, Vol 2021 (2021)
Publication Year :
2021
Publisher :
Wiley, 2021.

Abstract

In this paper, we investigate the following Kirchhoff type problem involving the fractional px-Laplacian operator. a−b∫Ω×Ωux−uypx,y/px,yx−yN+spx,ydxdyLu=λuqx−2u+fx,ux∈Ωu=0 x∈∂Ω,, where Ω is a bounded domain in ℝN with Lipschitz boundary, a≥b>0 are constants, px,y is a function defined on Ω¯×Ω¯, s∈0,1, and qx>1, Lu is the fractional px-Laplacian operator, N>spx,y, for any x,y∈Ω¯×Ω¯, px∗=px,xN/N−spx,x, λ is a given positive parameter, and f is a continuous function. By using Ekeland’s variational principle and dual fountain theorem, we obtain some new existence and multiplicity of negative energy solutions for the above problem without the Ambrosetti-Rabinowitz ((AR) for short) condition.

Subjects

Subjects :
Mathematics
QA1-939

Details

Language :
English
ISSN :
23148896 and 23148888
Volume :
2021
Database :
Directory of Open Access Journals
Journal :
Journal of Function Spaces
Publication Type :
Academic Journal
Accession number :
edsdoj.103ab518fabc46469210f511d3069566
Document Type :
article
Full Text :
https://doi.org/10.1155/2021/8888078