Ground states of weighted 4D biharmonic equations with exponential growth

In this paper, we are concerned with the existence of a ground state solution for a logarithmic weighted biharmonic equation under Dirichlet boundary conditions in the unit ball B$$ B $$ of Double-struck capital R4$$ {\mathrm{\mathbb{R}}} circumflex 4 $$. The reaction term of the equation is assumed to have exponential growth, in view of Adams' type inequalities. It is proved that there is a ground state solution using min-max techniques and the Nehari method. The associated energy functional loses compactness at a certain level. An appropriate asymptotic condition allows us to bypass the non-compactness levels of the functional.