The authors prove the existence and local uniqueness of multi-peak solutions with prescribed L2 mass for the critical Brézis-Nirenberg problem in dimensions at least six.
Normalized Solutions to Schr\"{o}dinger Equations with General Nonlinearities in Bounded Domains via a Global Bifurcation Approach
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abstract
We obtain the existence, nonexistence and multiplicity of positive solutions with prescribed mass for nonlinear Schr\"{o}dinger equations in bounded domains via a global bifurcation approach. The nonlinearities in this paper can be mass supercritical, critical, subcritical or some mixes of these cases, and the equation can be autonomous or non-autonomous. This generalizes a result in Noris, Tavares and Verzini [\emph{Anal. PDE}, 7 (8) (2014) 1807-1838], where the equation is autonomous with homogeneous nonlinearities. Besides, we have proven some orbital stability or instability results.
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Existence and local uniqueness of multi-spike solutions for Br\'{e}zis-Nirenberg problem with prescribed mass
The authors prove the existence and local uniqueness of multi-peak solutions with prescribed L2 mass for the critical Brézis-Nirenberg problem in dimensions at least six.