CRITICAL GROWTH FRACTIONAL KIRCHHOFF ELLIPTIC PROBLEMS

Abstract

This article is concerned with the existence and multiplicity of positive weak solutions for the following fractional Kirchhoff-Choquard problem: (Formula presented) where Ω is open bounded domain of (Formula presented) with C2 boundary, N > 2s and s ∈ (0, 1), here M models Kirchhoff-type coefficient of the form M(t) = a + btθ−1, where a, b > 0 are given constants. (−∆)s is fractional Laplace operator, λ > 0 is a real parameter. We explore using the variational methods, the existence of solution for q ∈ (1, 2∗s) and θ ≥ 1. Here, (Formula presented) and (Formula presented) is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. © (2024), (Khayyam Publishing). All rights reserved.