Weighted biharmonic equations involving continous potentiel under exponential nonlinear growth

Abstract

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 in view of Adam's type inequalities. The weight $w(x)$ is of logarithm type and the potential $V$ is a positive continuous function on $\overline{B}$. It is proved that there is a nontrivial positive 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.

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• Ground state solutions for weighted biharmonic problem involving non linear exponential growth