Infinitely many nodal solutions for generalized logistic equations without odd symmetry on reaction. (June 2020)

• Record Type: Journal Article
• Authors: He, Tieshan; He, Lang; Huang, Yehui
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35J20 -- 35J60 -- 35J92 -- 58E05; Logistic type equation -- Nodal solution -- Variational approach -- Gradient flow -- Bifurcation-type theorem; 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.2019.111741
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider nonlinear parametric logistic type equations driven by a nonlinear nonhomogeneous differential operator. The reaction term is a Carathéodory function which is not assumed to be odd. The subdiffusive, equidiffusive and superdiffusive cases are all treated. We prove the existence of infinitely many nodal solutions. We also prove a bifurcation-type result describing the dependence of the set of constant sign solutions on the parameter in the superdiffusive case. Our approach uses variational methods together with upper-lower solutions and truncation techniques, and flow invariance arguments.