A Refined Approach for Non-Negative Entire Solutions of Δ u + up = 0 with Subcritical Sobolev Growth

Authors

John Villavert, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

2-2017

Abstract

Let N≥2and 1uis a non-negative classical solution of the Lane–Emden equation, thenu≡0. The method of moving planes combined with the Kelvin transform provides an elegant proof of this theorem. A classical approach of Serrin and Zou, originally used for the Lane–Emden system, yields another proof but only in lower dimensions. Motivated by this, we further refine this approach to find an alternative proof of the Liouville type theorem in all dimensions.

Comments

© 2017 Walter de Gruyter GmbH, Berlin/Boston. Original published version available at https://doi.org/10.1515/ans-2016-6024

Recommended Citation

Villavert, J. (2017). A Refined Approach for Non-Negative Entire Solutions of Δ u + up = 0 with Subcritical Sobolev Growth, Advanced Nonlinear Studies, 17(4), 691-703. doi: https://doi.org/10.1515/ans-2016-6024

First Page

691

Last Page

703

Publication Title

Advanced Nonlinear Studies

DOI

10.1515/ans-2016-6024