We study a weighted $\frac{ N}{ 2}$ biharmonic equation involving a positive continuous potential in $\overline{ B}$. The non-linearity is assumed to have critical exponential growth in view of logarithmic weighted Adams' type inequalities in the unit ball of $\mathbb{ R}^{ N}$. It is proved that there is a nontrivial weak solution to this problem by the mountain Pass Theorem. We avoid the loss of compactness by proving a concentration compactness result and by a suitable asymptotic condition.
Categories: math.AP