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arXiv · 2201.10433

Weighted biharmonic equations involving continous potentiel under exponential nonlinear growth

Brahim Dridi·Rached Jaidane
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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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Brahim Dridi, Rached Jaidane. 2022-01-25. Weighted biharmonic equations involving continous potentiel under exponential nonlinear growth. https://doi.org/10.1007/s00009-023-02301-9

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