Abstract
This paper deals with the qualitative analysis of solutions to the following $(p,q)$-fractional equation:\begin{equation*}(-\Delta)^{s_1}_{p}u+(-\Delta)^{s_2}_{q}u+V(x) \big(|u|^{p-2}u+|u|^{q-2}u\big) = K(x)\frac{f(u)}{|x|^\beta} \quad \text{in } \mathbb R^N,\end{equation*}where $1< q< p$, $0< s_2\leq s_1< 1$, $ps_1=N$, $\beta\in[0,N)$, and $V,K\colon \mathbb R^N\to\mathbb R$, $f\colon \mathbb R\to \mathbb R$ are continuous functions satisfying some natural hypotheses. We are concerned both with the case when $f$ has a subcritical growth and with the critical framework with respect to the exponential nonlinearity. By combining a Moser-Trudinger type inequality for fractional Sobolev spaces with Schwarz symmetrization techniques and related variational and topological methods, we prove the existence of nonnegative solutions.
Citation
Deepak Kumar. Vicenţiu D. Rădulescu. Konijeti Sreenadh. "Unbalanced fractional elliptic problems with exponential nonlinearity: subcritical and critical cases." Topol. Methods Nonlinear Anal. 59 (1) 277 - 302, 2022. https://doi.org/10.12775/TMNA.2021.026
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