Year: 2022
Author: Qing Guo, Lixiu Duan
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 3 : pp. 259–280
Abstract
This paper, we study the multiplicity of solutions for the fractional Schrödinger equation
\begin{equation*}(-\Delta)^su+V(x)u=u^p,\ \ u>0,\ \ x\in\mathbb{R}^N,\ \ u\in H^s(\mathbb{R}^N),\end{equation*}
with $s\in(0,1),\ N\geq3,\ p\in(1,\frac{2N}{N-2s}-1)$ and $\lim_{|y|\rightarrow+\infty}V(y)>0$. By assuming suitable decay property of the radial potential $V(y)=V(|y|)$, we construct another type of solutions concentrating at infinite vertices of two similar equilateral polygonal with infinitely large length of sides. Hence, besides the length of each polygonal, we must consider one more parameter, that is the height of the podetium, simultaneously. Another difficulty lies in the non-local property of the operator $(-\Delta)^s$ and the algebraic decay involving the approximation solutions make the estimates become more subtle.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v35.n3.5
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 3 : pp. 259–280
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Fractional Schrödinger equations infinitely many solutions reduction method.