Constructing solutions for the prescribed scalar curvature problem via local Pohozaev identities
| Autor: | Chunhua Wang, Shuangjie Peng, Suting Wei |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Reduction (recursion theory)
Applied Mathematics Prescribed scalar curvature problem 010102 general mathematics Type (model theory) 01 natural sciences Critical point (mathematics) 010101 applied mathematics Combinatorics Arbitrarily large Saddle point Bounded function 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Differential Equations. 267:2503-2530 |
| ISSN: | 0022-0396 |
| Popis: | This paper deals with the following prescribed scalar curvature problem − Δ u = Q ( | y ′ | , y ″ ) u N + 2 N − 2 , u > 0 , y = ( y ′ , y ″ ) ∈ R 2 × R N − 2 , where Q ( y ) is nonnegative and bounded. By combining a finite reduction argument and local Pohozaev type of identities, we prove that if N ≥ 5 and Q ( r , y ″ ) has a stable critical point ( r 0 , y 0 ″ ) with r 0 > 0 and Q ( r 0 , y 0 ″ ) > 0 , then the above problem has infinitely many solutions, whose energy can be made arbitrarily large. Here, instead of estimating directly the derivatives of the reduced functional, we apply some local Pohozaev identities to locate the concentration points of the bump solutions. Moreover, the concentration points of the bump solutions include a saddle point of Q ( y ) . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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