MULTIPLE SOLUTIONS FOR A CLASS OF NONHOMOGENEOUS SEMILINEAR EQUATIONS WITH CRITICAL CONE SOBOLEV EXPONENT, By Mohsen Alimohammady

Research

Title	MULTIPLE SOLUTIONS FOR A CLASS OF NONHOMOGENEOUS SEMILINEAR EQUATIONS WITH CRITICAL CONE SOBOLEV EXPONENT
Type	Article
Keywords	Semilinear equations, degenerate differential operator, partial differential equation on manifold
Journal	PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
DOI	10.1090/proc/14332
Researchers	Morteza Koozehgar (First researcher) , Mohsen Alimohammady (Second researcher) , A.A. Jafari (Third researcher)

Abstract

In this paper, we deal with the study of a class of semilinear and nonhomogeneous Schr¨odinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and the critical cone Sobolev exponent with respect to the nonhomogeneous term g(x) ∈ L n 2 2 (B). Our approach improves on and generalizes the previous results in [Indian J. Pure Appl. Math. 48 (2017), pp. 133–146] and [Ann. Global Anal. Geom. 39 (2011), pp. 27–43]