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Mohsen Alimohammady

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

Research

Title
Multiple solutions for non-homogeneous degenerate Schrödinger equations in cone Sobolev spaces
Type
JournalPaper
Keywords
Semilinear elliptic equation, non-homogeneous Schrödinger equation, degenerate elliptic equations, cone Sobolev space
Year
2017
Journal INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
DOI
Researchers Mohsen Alimohammady ، َAli Asghar Jafari ، Morteza Koozehgar

Abstract

The present paper deals with the study of semilinear and non-homogeneous Schrödinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and for p ∈ (2, 2∗) with respect to non-homogeneous term g(x) ∈ L2n/2(B), which helps to find multiple solutions of our problem. More precisely, we prove the existence of two solutions to the problem 1.1 with negative and positive energy in cone Sobolev space H2,01,n/2 (B). Finally, we consider p = 2 and we prove the existence and uniqueness of Fuchsian-Poisson problem