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arXiv · 2311.16786

A Logarithmic Weighted Adams-type inequality in the whole of $\mathbb{R}^{N}$ with an application

Rached Jaidane
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Abstract

In this paper, we will establish a logarithmic weighted Adams inequality in a logarithmic weighted second order Sobolev space in the whole set of $\mathbb{R}^{N}$. Using this result, we delve into the analysis of a weighted fourth-order equation in $\mathbb{R}^{N}$. We assume that the non-linearity of the equation exhibits either critical or subcritical exponential growth, consistent with the Adams-type inequalities previously established. By applying the Mountain Pass Theorem, we demonstrate the existence of a weak solution to this problem. The primary challenge lies in the lack of compactness in the energy caused by the critical exponential growth of the non-linear term $f$.

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Rached Jaidane. 2023-11-28. A Logarithmic Weighted Adams-type inequality in the whole of $\mathbb{R}^{N}$ with an application. https://arxiv.org/abs/2311.16786

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