On a weighted problem of p-biharmonic type in the unit ball of R^N with exponential growth non linearity

In this paper, we are concerned with the existence of a ground state solution for a logarithmic weighted p-biharmonic equation under Dirichlet boundary conditions in the unit ball $B$ of $\mathbb{R}^{N}$. 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.