Open Access
Translator Disclaimer
2016 Construction of sign-changing solutions for a subcritical problem on the four dimensional half sphere
Rabeh Ghoudi, Kamal Ould Bouh
Tohoku Math. J. (2) 68(4): 591-605 (2016). DOI: 10.2748/tmj/1486177217

Abstract

This paper is devoted to studying the nonlinear problem with subcritical exponent $(S_\varepsilon) : -\Delta_g u+2u = K|u|^{2-\varepsilon}u$, in $ S^4_+ $, ${\partial u}/{\partial\nu} =0$, on $\partial S^4_+,$ where $g$ is the standard metric of $S^4_+$ and $K$ is a $C^3$ positive Morse function on $\overline{S_+^4}$. We construct some sign-changing solutions which blow up at two different critical points of $K$ in interior. Furthermore, we construct sign-changing solutions of $(S_\varepsilon)$ having two bubbles and blowing up at the same critical point of $K$.

Citation

Download Citation

Rabeh Ghoudi. Kamal Ould Bouh. "Construction of sign-changing solutions for a subcritical problem on the four dimensional half sphere." Tohoku Math. J. (2) 68 (4) 591 - 605, 2016. https://doi.org/10.2748/tmj/1486177217

Information

Published: 2016
First available in Project Euclid: 4 February 2017

zbMATH: 1380.35092
MathSciNet: MR3605449
Digital Object Identifier: 10.2748/tmj/1486177217

Subjects:
Primary: 35J20
Secondary: 35J60

Keywords: Bubble-tower solutions , critical points , Scalar curvature , variational problem

Rights: Copyright © 2016 Tohoku University

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.68 • No. 4 • 2016
Back to Top