Oscillating solutions for nonlinear equations involving the Pucci's extremal operators. (October 2020)

• Record Type: Journal Article
• Authors: d'Avenia, Pietro; Pomponio, Alessio
• Is Part Of: Nonlinear analysis. Volume 55(2020)
• Publication Date: 2020-10
• Subjects: Pucci's extremal operators -- Fully nonlinear operator equations -- Oscillating solutions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103118
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper deals with the following nonlinear equations M λ, Λ ± ( D 2 u ) + g ( u ) = 0 i n R N, where M λ, Λ ± are the Pucci's extremal operators, for N ⩾ 1 and under the assumption g ′ ( 0 ) > 0 . We show the existence of oscillating solutions, namely with an unbounded sequence of zeros. Moreover these solutions are periodic, if N = 1, while they are radial symmetric and decay to zero at infinity with their derivatives, if N ⩾ 2 .