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HOME > Table of Contents and Abstracts > Vol. 68, No. 4
Tohoku Mathematical Journal
2016
December
SECOND SERIES VOL. 68, NO. 4
Tohoku Math. J.
68 (2016), 591-605
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Title
CONSTRUCTION OF SIGN-CHANGING SOLUTIONS FOR A SUBCRITICAL PROBLEM ON THE FOUR DIMENSIONAL HALF SPHERE
Author
Rabeh Ghoudi and Kamal Ould Bouh
(Received September 22, 2014, revised March 5, 2015) |
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 $K$.
Mathematics Subject Classification.
Primary 35J20; Secondary 35J60.
Key words and phrases.
Critical points, Variational problem, Scalar curvature, Bubble-tower solutions.
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