On doubly nonlocal $p$-fractional coupled elliptic system

Abstract

We study the following nonlinear system with perturbations involving p-fractional Laplacian R), i = 1, 2 and f 1 , f 2 : R n → R are perturbations. We show existence of atleast two nontrivial solutions for (P ) using Nehari manifold and minimax methods.

Combined effects of Choquard and singular nonlinearities in fractional Kirchhoff problems

“…For recent results about fractional Kirchho problems, we refer to [10, 19-23, 28-30, 49, 50] and the references cited there. In recent years, much attention has been focused on the existence and properties of nontrivial solutions for fractional Choquard equation involving fractional p−Laplacian,see for example [37,41,47,51]. In [37], Mukherjee and Sreenadh studied the following subcritical Choquard system involving fractional p−Laplacian and perturbations…”

Critical growth elliptic problems with Choquard type nonlinearity:A survey

“…There are not many results on elliptic systems with non-homogeneous nonlinearities in the literature but we cite [19,24,63] as some very recent works on the study of fractional elliptic systems. Motivated by these articles, we consider the following nonhomogenous quasilinear system of equations with perturbations involving p-fractional Laplacian in [54]:…”

Multiple Solutions for a Fractional Laplacian System Involving Critical Sobolev-Hardy Exponents and Homogeneous Term

“…We show that the system (1.1) has at least two positive solutions when the parameters λ, µ and weight functions f , g satisfied some certain conditions. It should be mentioned that in [8,9,10,15,22], some problems involving fractional Laplacian operator were investigated by the Nehari manifold and fibering method. We look for solutions of (1.1) in the Sobolev space From (2.2), we employ the following equivalent norm in X s 0 (Ω):…”