Infinitely many positive solutions for a -Kirchhoff-type equation

This paper is concerned with the existence of infinitely many positive solutions to a class of p ( x ) -Kirchhoff-type problem. By means of a direct variational approach and the theory of the variable exponent Sobolev spaces, we establish the existence of infinitely many distinct positive solutions whose W 1 , p ( x ) ( Ω ) -norms and L ∞ -norms tend to zero under suitable hypotheses about nonlinearity.