Critical growth elliptic problems with Choquard type nonlinearity:A survey

2018/11/11 by Tuhina Mukherjee, Mukherjee, Tuhina, K. Sreenadh +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1811.04353

openalex publication_date 2018/11/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

This article deals with a survey of recent developments and results on Choquard equations where we focus on the existence and multiplicity of solutions of the partial differential equations which involve the nonlinearity of convolution type. Because of its nature, these equations are categorized under the nonlocal problems. We give a brief survey on the work already done in this regard following which we illustrate the problems we have addressed. Seeking the help of variational methods and asymptotic estimates, we prove our main results.

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