2024 : 12 : 22
Mohsen Alimohammady

Mohsen Alimohammady

Academic rank: Professor
ORCID:
Education: PhD.
ScopusId:
HIndex:
Faculty: Faculty of Mathematical Sciences
Address:
Phone: 011-35302462

Research

Title
Existence and multiplicity solutions for a singular elliptic p(x)-Laplacian equation
Type
JournalPaper
Keywords
p(x)-Laplacian, variational method, genus theory, Sobolev space
Year
2024
Journal Tamkang Journal of Mathematics
DOI
Researchers S Abolfazli ، Mohsen Alimohammady ، Asieh Rezvani

Abstract

This paper deals with the existence and multiplicity of nontrivial weak solutions for the following equation involving variable exponents:    − △p(x) u + |u| r−2u |x| r = λh(x, u), in Ω, u = 0, on ∂Ω, where Ω is a bounded domain of R N with smooth enough boundary which is subject to Dirichlet boundary condition. Using a variational method and Krasnoselskii’s genus theory, we would show the existence and multiplicity of the solutions. Next, we study closedness of set of eigenfunctions, such that p(x) ≡ p.