Infinitely many solution for prescribed curvature problem on $S^N$

By Jun-cheng Wei, Shusen Yan. 2008

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We consider the following prescribed scalar curvature problem on $ S^N$ (*)$$\left\{\begin{array}{l} - \Delta_{S^N} u + \frac{N(N-2)}{2} u = \tilde{K} u^{\frac{N+2}{N-2}} {on} S^N, u>0 \end{array}\right. $$ where $ \tilde{K}$ is positive and rotationally symmetric. We show that if $\tilde{K}$ has a local maximum point between the poles then equation (*) has {\bf infinitely many non-radial positive} solutions, whose energy can be made arbitrarily large.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0826f0f4903d17059acdbd78651f7fe4c297bba2

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Large energy entire solutions for the yamabe equation (2011, background): “We point out that the idea of using the (large) number of bubbles as a parameter of the problem has been previously developed by Wei and Yan in [18] for critical problems with the presence of weights.”