Elliptic differential inclusions on non-compact Riemannian manifolds. (February 2023)

• Record Type: Journal Article
• Authors: Kristály, Alexandru; Mezei, Ildikó I.; Szilák, Károly
• Is Part Of: Nonlinear analysis. Volume 69(2023)
• Publication Date: 2023-02
• Subjects: Differential inclusions -- Riemannian manifolds -- Variational arguments -- Isometries; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103740
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We investigate a large class of elliptic differential inclusions on non-compact complete Riemannian manifolds which involves the Laplace–Beltrami operator and a Hardy-type singular term. Depending on the behavior of the nonlinear term and on the curvature of the Riemannian manifold, we guarantee non-existence and existence/multiplicity of solutions for the studied differential inclusion. The proofs are based on nonsmooth variational analysis as well as isometric actions and fine eigenvalue properties on Riemannian manifolds. The results are also new in the smooth setting.