Infinitely many solutions for fractional Schrödinger equation with potential vanishing at infinity View Full Text


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Article Info

DATE

2019-03-27

AUTHORS

Yongzhen Yun, Tianqing An, Jiabin Zuo, Dafang Zhao

ABSTRACT

The paper investigates the following fractional Schrödinger equation: (−Δ)su+V(x)u=K(x)f(u),x∈RN,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{aligned} (-\Delta )^{s}u+V(x)u=K(x)f(u), \quad x\in \mathbb{R}^{N}, \end{aligned}$$ \end{document} where 0\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(-\Delta )^{s}$\end{document} is the fractional Laplacian operator of order s. V(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$V(x)$\end{document}, K(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$K(x)$\end{document} are nonnegative continuous functions and f(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f(x)$\end{document} is a continuous function satisfying some conditions. The existence of infinitely many solutions for the above equation is presented by using a variant fountain theorem, which improves the related conclusions on this topic. The interesting result of this paper is the potential V(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$V(x)$\end{document} vanishing at infinity, i.e., lim|x|→+∞V(x)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lim_{|x|\rightarrow +\infty }V(x)=0$\end{document}. More... »

PAGES

62

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13661-019-1175-3

DOI

http://dx.doi.org/10.1186/s13661-019-1175-3

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https://app.dimensions.ai/details/publication/pub.1113046386


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