Existence and nonexistence of sign-changing solutions for singular semilinear equations on exterior domains. (April 2022)

• Record Type: Journal Article
• Authors: Iaia, Joseph A.
• Is Part Of: Nonlinear analysis. Volume 217(2022)
• Publication Date: 2022-04
• Subjects: Sign-changing -- Multiple solutions -- Sublinear -- Exterior domains; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112752
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study solutions of Δ u + K ( | x | ) f ( u ) = 0 in the exterior of the ball of radius R > 0 in R N where f grows sublinearly at infinity and is singular at 0 with f ( u ) ∼ − 1 | u | q − 1 u, 0 < q < 1, for small u . We assume K ( | x | ) ∼ | x | − α for large | x | and establish existence of positive and sign-changing solutions when α > 2 ( N − 1 ) and R > 0 is small. We prove nonexistence when R > 0 is large and we also prove nonexistence for 2 < α < N + q ( N − 2 ) and all R > 0 .