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arXiv · 2412.03296

Normalized solutions on large smooth domains to the Schr\"{o}dinger equations with potential and combined nonlinearities: The Sobolev critical case

Xiaolu Lin·Yanjun Liu·Zongyan Lv
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Abstract

In this paper, we consider the existence and multiplicity of prescribed mass solutions to the following nonlinear Schrodinger equations with mixed nonlinearities. The standard approach based on the Pohozaev identity to obtain normalized solutions is invalid as the presence of potential. Besides, Our study can be regarded as a Sobolev critical case complement of Bartsch-Qi-Zou (Math Ann 390, 4813-4859, 2024), which has addressed an open problem raised in Bartsch et al.(Commun Partial Differ Equ 46(9):1729--1756,2021).

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Xiaolu Lin, Yanjun Liu, Zongyan Lv. 2024-12-04. Normalized solutions on large smooth domains to the Schr\"{o}dinger equations with potential and combined nonlinearities: The Sobolev critical case. https://arxiv.org/abs/2412.03296

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