Polyharmonic Kirchhoff problems involving exponential non-linearity of Choquard type with singular weights. (July 2020)

• Record Type: Journal Article
• Authors: Arora, R.; Giacomoni, J.; Mukherjee, T.; Sreenadh, K.
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: 35R10 -- 35R09 -- 35J60 -- 35A15 -- 35J35; Doubly non local equation -- Kirchhoff term -- Choquard non-linearity with singular weights -- Singular Adams–Moser inequality -- Nehari manifold -- Polyharmonic operator; 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.2020.111779
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this work, we study the higher order Kirchhoff type Choquard equation ( K C ) involving a critical exponential non-linearity and singular weights. We prove the existence of solution to ( K C ) using Mountain pass Lemma in light of Moser–Trudinger and singular Adams–Moser inequalities. In the second part of the paper, using the Nehari manifold technique and minimization over its suitable subsets, we prove the existence of at least two solutions to the Kirchhoff type Choquard equation ( P λ, M ) involving convex–concave type non-linearity.