| Abstract: |
| In this talk, we will discuss the existence of normalized solutions for Sobolev critical Schr\odinger equations within general bounded domains. While recent studies have extensively explored normalized solutions in whole spaces, less is known about their existence in bounded domains. By integrating a recent abstract minimax principle, which incorporates Morse index information for constrained functionals, with novel blow-up analyses, we will demonstrate the existence of normalized solutions of the mountain pass type. |
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