Existence of solution to Kirchhoff type problem with gradient nonlinearity and a perturbation term

Abstract

This article deals with the existence of a weak solution to the Kirchhoff problem:

where is a bounded and smooth domain in . We assume that f, h and A are continuous functions and the growth of the non linearity is dependent on u and . We do not assume any growth condition on the perturbation term h. In the case of we consider the exponential growth in the second variable of f. The proof of our main existence result uses an iterative technique based on the mountain pass theorem.