Details

Autor(en) / Beteiligte

• Felmer, Patricio
• Quaas, Alexander
• Tan, Jinggang

Titel

Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian

Ist Teil von

• Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2012-12, Vol.142 (6), p.1237-1262

Ort / Verlag

Edinburgh, UK: Royal Society of Edinburgh Scotland Foundation

Erscheinungsjahr

2012

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We study the existence of positive solutions for the nonlinear Schrödinger equation with the fractional Laplacian \begin{gather*}(-\Delta)^{\alpha}u+u=f(x,u)\text{~in~}\mathbb{R}^{N},\\u>0\text{~in~}\mathbb{R}^{N},\qquad\lim_{|x|\rightarrow\infty}u(x)=0.\end{gather*} Furthermore, we analyse the regularity, decay and symmetry properties of these solutions.