June 2023 EXISTENCE OF SOLUTIONS TO SEMILINEAR ELLIPTIC EQUATIONS WITH VARIABLE EXPONENT SINGULARITY
Ambesh Kumar Pandey, Rasmita Kar
Rocky Mountain J. Math. 53(3): 903-913 (June 2023). DOI: 10.1216/rmj.2023.53.903

Abstract

In this article, our interest is to prove the existence of positive solutions to the semilinear elliptic problem

div(A(x)u)λu|x|2=f(x)uη(x) in Ω,u=0 on Ω.

Here ΩN (N3) is a bounded domain with 0Ω, 0λ<((N2)(2))2 and 0<η(x)C1(Ω¯). The function f>0 is in suitable Lebesgue spaces. The given problem is notable due to the presence of the variable exponent η(x), and it has singularities on the boundary of the domain as well as at the origin.

Citation

Download Citation

Ambesh Kumar Pandey. Rasmita Kar. "EXISTENCE OF SOLUTIONS TO SEMILINEAR ELLIPTIC EQUATIONS WITH VARIABLE EXPONENT SINGULARITY." Rocky Mountain J. Math. 53 (3) 903 - 913, June 2023. https://doi.org/10.1216/rmj.2023.53.903

Information

Received: 25 March 2022; Revised: 20 July 2022; Accepted: 20 July 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617920
zbMATH: 07731154
Digital Object Identifier: 10.1216/rmj.2023.53.903

Subjects:
Primary: 35B45 , 35J25 , 35J61 , 35J75

Keywords: a priori estimate , Hardy inequality , singularity , ‎variable exponent

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
11 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.53 • No. 3 • June 2023
Back to Top