An existence result for a Robin problem involving $p(x)$-Kirchhoff-type equation with indefinite weight

This paper discusses the existence of at least two distinct nontrivial weak solutions for a class of $p(x)$-Kirchhoff-type equation plus an indefinite potential under Robin boundary condition. The variable exponent theory of generalized Lebesgue-Sobolev spaces, mountain pass theorem and Ekeland variational principle are used for this purpose.