Generalized Fountain Theorem for Locally Lipschitz Functionals and application. (September 2022)

• Record Type: Journal Article
• Authors: Alves, Claudianor O.; Batkam, Cyril J.; Patricio, Geovany F.
• Is Part Of: Nonlinear analysis. Volume 222(2022)
• Publication Date: 2022-09
• Subjects: primary 35J15 35J20 -- secondary 26A27; Noncooperative elliptic system -- Variational methods -- Fountain Theorem -- Discontinuous nonlinearity; 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.2022.112982
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we obtain a nonsmooth version of the infinite-dimensional Fountain Theorem established by Batkam and Colin (2013). No symmetry condition on the energy functional is needed in our formulation. As an application, we prove the existence of multiple solutions for the following class of elliptic system ( S ) Δ u − u ∈ [ f ̲ ( x, u, v ), f ¯ ( x, u, v ) ] a.e in R N − Δ v + v ∈ [ g ̲ ( x, u, v ), g ¯ ( x, u, v ) ] a.e in R N, u, v ∈ H 1 ( R N ), where f and g are measurable functions that satisfy some technical conditions.