Multiplicity of positive solutions for a problem of Kirchhoff type involving variable exponent ℓ (·)-Laplacian-Like operators

In this paper, we investigate the existence of infinitely many positive solutions for a class of Kirchhoff-type problems involving a ℓ(·)-Laplacian-like operator. Using a direct variational method and the framework of variable exponent Sobolev spaces, we prove the existence of infinitely many distinct positive solutions. Moreover, under suitable assumptions on the nonlinearity, the W1,ℓ(·) (D)-norms and L∞-norms of these solutions are shown to tend to zero.