Abstract
In this work, we study the weighted Kirchhoff problemwhere B is the unit ball in R2, sigma(x) = log e |x|, the singular logarithm weight in the Trudinger-Moser embedding, g is a continuous positive function on R+ and the potential V is a continuous positve function. The nonlinearities are critical or subcritical growth in view of Trudinger-Moser inequalities. We prove the existence of non-trivial solutions via the critical point theory. In the critical case, the associated energy function does not satisfy the condition of compactness. We provide a new condition for growth and we stress its importance to check the min-max compactness level.