An abstract sub-supersolution method in partially ordered spaces. (April 2023)

• Record Type: Journal Article
• Authors: Fresse, Lucas; Motreanu, Viorica V.
• Is Part Of: Nonlinear analysis. Volume 70(2023)
• Publication Date: 2023-04
• Subjects: Sub-supersolution method -- Partially ordered spaces -- Quasilinear boundary value problems; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103784
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We present a general framework in which sub-supersolution techniques can be applied. Specifically, we consider a normed vector space endowed with a partial order. This allows us to introduce a notion of sub- and supersolutions relative to an equation driven by operators defined from the space to its topological dual. We provide sufficient conditions to guarantee that the interval determined by an ordered pair of sub-supersolutions contains a solution of the initial problem. We also study existence of extremal positive or negative solutions and location of nodal solutions. Examples of applications to quasilinear boundary value problems are given.