Infinitely many solutions for the prescribed scalar curvature problem on SN
By Jun-cheng Wei, Shusen Yan. 2010
201 citations recorded by the source corpus.
Abstract We consider the following prescribed scalar curvature problem on S N (∗) { − Δ S N u + N ( N − 2 ) 2 u = K ˜ u N + 2 N − 2 on S N , u > 0 where K ˜ is positive and rotationally symmetric. We show that if K ˜ has a local maximum point between the poles then Eq. (∗) has infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.
Subfields: Applied Mathematics, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/a6b99a9529622c5216b6305deacc56875d2ed2f3
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In Applied Mathematics
- Shuangjie Peng
- Shusen Yan
- Jun-cheng Wei
- Changshou Lin
- Zhi-Qiang Wang
- Yinbin Deng
- A. Malchiodi
- Manuel del Pino
In Mathematical Physics
- Shuangjie Peng
- Jun-cheng Wei
- Zhi-Qiang Wang
- Changshou Lin
- Shusen Yan
- Yinbin Deng
- Louis Jeanjean
- Thomas Bartsch
In Nuclear and High Energy Physics
Citations in the corpus
- On the prescribed scalar curvature problem in RN, local uniqueness and periodicity (2015, methodology): “Then with careful estimates of uk in some weighted L ∞ spaces similar to those used in [19], they proved that uk converges locally in R to a solution u of the form (1.”
- Sharp quantitative estimates of Struwe’s decomposition (2021, unknown): “SHARP QUANTITATIVE ESTIMATES 49 [34] Juncheng Wei and Shusen Yan.”
- Infinitely many positive solutions for an elliptic problem with critical or supercritical growth (2011, background): “Since this part is similar to [19], we shall only give a sketch of the proofs.”
- Segregated and Synchronized Vector Solutions for Nonlinear Schrödinger Systems (2013, methodology): “Our methods are inspired by the work of [31,33] for scalar nonlinear elliptic equations.”