Existence and multiplicity of solutions for nonlocal fourth-order p ( x )-Kirchhoff problems with Leray--Lions operators, Hardy potentials, and logarithmic nonlinearities

This paper is devoted to the existence and multiplicity of weak solutions for a class of nonlocal fourth-order p ⁢ ( x ) {p(x)} -Kirchhoff problems involving a Leray–Lions type operator, Hardy-type singular potentials, and logarithmic nonlinear reaction terms in the framework of variable exponent Sobolev spaces. More precisely, we investigate the boundary value problem geändert { M ⁢ ( ∫ Ω A ⁢ ( x , Δ ⁢ u ) ⁢ 𝑑 x ) ⁢ Δ ⁢ ( a ⁢ ( x , Δ ⁢ u ) ) + θ ⁢ ( x ) ⁢ | u | s ⁢ ( x ) - 2 ⁢ u | x | 2 ⁢ s ⁢ ( x ) + c ⁢ ( x ) ⁢ | u | q ⁢ ( x ) -