Weighted fourth order equation of Kirchhoff type in dimension 4 with non-linear exponential growth - Jaidane, Rached (Topological Methods in Nonlinear Analysis, 2023)
In this work, we are concerned with the existence of a ground state solution for a Kirchhoff weighted problem under boundary Dirichlet condition in the unit ball of $\mathbb{R}^{4}$. The nonlinearities have critical growth in view of Adams' inequalities. To prove the existence result, we use Pass Mountain Theorem.The main difficulty isthe loss of compactness due to the critical exponential growth of the nonlinearterm $f$. 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.