Classification of positive smooth solutions to third-order PDEs involving fractional Laplacians

with $Ḣ^{\frac{3}{2}}$ -critical nonlinearity. By showing the equivalence between the PDEs and the corresponding integral equations and using results from Chen et al. (2006) and Dai et al. (2018), we prove that positive classical solutions $u$ to the above equations are radially symmetric about some point $x_{0} \in ℝ^{d}$ and derive the explicit forms for $u$ .

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Keywords

fractional Laplacians, odd order, positive smooth solutions, radial symmetry, uniqueness, equivalence

Mathematical Subject Classification 2010

Primary: 35R11

Secondary: 35B06, 35J91

Milestones

Received: 21 July 2017

Revised: 31 January 2018

Accepted: 3 February 2018

Published: 11 April 2018

Authors

Wei Dai
School of Mathematics and Systems Science Beihang University (BUAA) Beijing China

Guolin Qin
School of Mathematics and Systems Science Beihang University (BUAA) Beijing China

Vol. 295, No. 2, 2018

Wei Dai and Guolin Qin

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors