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arXiv · 1510.06926

Concentration phenomena for fractional elliptic equations involving exponential critical growth

Claudianor O. Alves·João Marcos do Ó·Olímpio H. Miyagaki
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Abstract

In this paper, we deal with the following singular perturbed fractional elliptic problem $ ε^{} (-Δ)^{1/2}{u}+V(z)u=f(u)\,\,\, \mbox{in} \,\,\, \mathbb{R}, $ where $ (-Δ)^{1/2}u$ is the square root of the Laplacian and $f(s)$ has exponential critical growth. Under suitable conditions on $f(s)$, we construct a localized bound state solution concentrating at an isolated component of the positive local minimum points of the potential of $V$ as $ε$ goes to $0.$

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Claudianor O. Alves, João Marcos do Ó, Olímpio H. Miyagaki. 2015-10-23. Concentration phenomena for fractional elliptic equations involving exponential critical growth. https://arxiv.org/abs/1510.06926

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