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Fractional interpolation inequality and radially symmetric ground states

Published online by Cambridge University Press:  12 May 2022

Li Ma
Affiliation:
School of Mathematics and Physics, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing 100083, China (lma17@ustb.edu.cn,dfangyuan20@163.com)
Fangyuan Dong
Affiliation:
School of Mathematics and Physics, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing 100083, China (lma17@ustb.edu.cn,dfangyuan20@163.com)

Abstract

In this paper, we establish a new fractional interpolation inequality for radially symmetric measurable functions on the whole space $R^{N}$ and a new compact imbedding result about radially symmetric measurable functions. We show that the best constant in the new interpolation inequality can be achieved by a radially symmetric function. As applications of this compactness result, we study the existence of ground states of the nonlinear fractional Schrödinger equation on the whole space $R^{N}$. We also prove an existence result of standing waves and prove their orbital stability.

Type
Research Article
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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