Combined effects of Choquard and singular nonlinearities in fractional Kirchhoff problems

Abstract

The aim of this paper is to study the existence and multiplicity of solutions for a class of fractional Kirchho problems involving Choquard type nonlinearity and singular nonlinearity. Under suitable assumptions, two nonnegative and nontrivial solutions are obtained by using the Nehari manifold approach combined with the Hardy-Littlehood-Sobolev inequality.

The existence of positive solutions for the Neumann problem of p-Laplacian elliptic systems with Sobolev critical exponent

“…In recent years, the problem of elliptic equations (systems) with critical exponents has attracted the attention of many researchers, and related theory has also made great progress, e.g., results on the existence and nonexistence of nontrivial and multiple solutions were proved, and also some properties of solutions (see [2][3][4][5][6][7][8]). At the same time, in recent years, the problem with critical exponents in fractional elliptic equations, such as fractional Kirchhoff problems and Schrödinger-Kirchhoff-type problems involving the fractional p-Laplacian, have also attracted the attention of researchers (see [9][10][11]).…”

A study of extremal parameter for fractional singular Choquard problem

“…where 𝛾 > 0, 𝑁 ≥ 2𝑠, 𝑠 ∈ (0, 1), 1 < 𝑝 ≤ 2 * 𝜇,𝑠 − 1, and Ω is a smooth bounded domain in ℝ 𝑁 have not been explored in much extent. We cite [38], where the nonlinearity has subcritical growth, authors have proved existence of two positive weak solutions using the Nehari manifold technique. Recently in [36], Sousa et al have shown the existence of a solution for the weighted singular fractional differential problem involving 𝑝-Laplace equation using the Nehari manifold method.…”

Initial Boundary Value Problem for a Fractional Viscoelastic Equation of the Kirchhoff Type

“…Moreover, they obtained the existence of infinitely many pairs of entire solutions by genus theory. Wang et al [16] studied the following fractional Kirchhoff equation involving Choquard nonlinearity and singular nonlinearity:…”