On a class of Kirchhoff problem involving Choquard nonlinearity with real parameter

Abstract

In this paper, we focus on investigating the existence and multiplicity of nontrivial weak solutions for a class of Choquard–Kirchhoff type equations. These equations involve a variable $s(x,\cdot)$-order fractional ($\tau_1(x,\cdot),\tau_2(x,\cdot)$)-Laplacian operator with a real parameter and a continuous variable parameter. The main challenges lie in the Choquard nonlinearities and Kirchhoff functions, along with the presence of double Laplace operators involving two variable parameters.