Infinitely many positive solutions for a p(x)-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 W1,p(x)(Ω)-norms and L∞-norms tend to zero under suitable hypotheses about nonlinearity.