Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions-Reference-Cited by-同舟云学术

Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions

Published:2024-05-17 Issue: Volume: Page:
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Guefaifia Rafik¹,Boulaaras Salah²,Jan Rashid³

Affiliation:

1. Department of Mathematics , College of Sciences , Qassim University , Buraydah , 51452 , Saudi Arabia ; and Laboratory of Mathematics, Informatics and Systems (LAMIS), Department of Mathematics and Computer Science, Echahid Cheikh Larbi Tebessi University, Tebessa, 12002, Algeria

2. Department of Mathematics , College of Sciences , Qassim University , Buraydah , 51452 , Saudi Arabia

3. Institute of Energy Infrastructure (IEI) , Department of Civil Engineering , College of Engineering , Universiti Tenaga Nasional (UNITEN) , Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang , Selangor , Malaysia ; and Mathematics Research Center, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey

Abstract

Abstract In this work, we establish a theorem concerning the extension of positive weak solutions for a stationary fractional Laplacian problem featuring weight functions that change sign. Additionally, we introduce novel conditions to ensure the existence of a positive solution for the given problem. These conditions are derived utilizing the approach of sub-super solutions, thereby extending and complementing existing results in the literature.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2024-2025/pdf

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