Existence solutions for a weighted equation of p-biharmonic type in the unit ball of $\mathbb{R}^{N}$ with critical exponential growth

Rached Jaidane

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arXiv · 2311.17125

Existence solutions for a weighted equation of p-biharmonic type in the unit ball of $\mathbb{R}^{N}$ with critical exponential growth

Rached Jaidane

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Abstract

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.

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Rached Jaidane. 2023-11-28. Existence solutions for a weighted equation of p-biharmonic type in the unit ball of $\mathbb{R}^{N}$ with critical exponential growth. https://arxiv.org/abs/2311.17125

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