N-Kirchhoff–Choquard equations with exponential nonlinearity. (September 2019)

• Record Type: Journal Article
• Authors: Arora, R.; Giacomoni, J.; Mukherjee, T.; Sreenadh, K.
• Is Part Of: Nonlinear analysis. Volume 186(2019)
• Page Start: 113
• Page End: 144
• Publication Date: 2019-09
• Subjects: 35R11 -- 35R09 -- 35A15; Doubly non local equation -- Kirchhoff equation -- Choquard nonlinearity with critical growth -- Moser–Trudinger inequality -- Nehari manifold; 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.2019.01.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This article deals with the study of the following Kirchhoff equation with exponential nonlinearity of Choquard type (see ( K C ) below). We use the variational method in the light of Moser–Trudinger inequality to show the existence of weak solutions to ( K C ) . Moreover, analyzing the fibering maps and minimizing the energy functional over suitable subsets of the Nehari manifold, we prove existence and multiplicity of weak solutions to convex–concave problem ( P λ, M ) below.