Existence Solutions for a Weighted Biharmonic Equation with Critical Exponential Growth

We deal with a weighted biharmonic problem in the unit ball of $\mathbb{R}^{4}$. The non-linearity is assumed to have critical exponential growth view Adam's type inequalities. weight $w(x)$ logarithm and potential $V$ positive continuous function on $\overline{B}$. It proved that there nontrivial weak solution this by mountain Pass Theorem. avoid loss compactness proving concentration result suitable asymptotic condition.