Normalized solutions for a class of Sobolev critical Schrodinger systems

Houwang Li; Tianhao Liu; Wenming Zou

Normalized solutions for a class of Sobolev critical Schrodinger systems

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arxiv 2410.15750 v1 pith:GIUXVA3H submitted 2024-10-21 math.AP

Houwang Li , Tianhao Liu , Wenming Zou This is my paper · ORCID

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This paper focuses on the existence and multiplicity of normalized solutions for the coupled Schrodinger system with Sobolev critical coupling term. We present several existence and multiplicity results under some explicit conditions. Furthermore, we present a non-existence result for the defocusing case. This paper, together with the paper [T. Bartsch, H. W. Li and W. M. Zou. Calc. Var. Partial Differential Equations 62 (2023) ], provides a more comprehensive understanding of normalized solutions for Sobolev critical systems. We believe our methods can also address the open problem of the multiplicity of normalized solutions for Schrodinger systems with Sobolev critical growth, with potential for future development and broader applicability.

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Multiple sign-changing and semi-nodal normalized solutions for a Gross-Pitaevskii type system on bounded domains: the $L^2$-supercritical case
math.AP 2025-06 conditional novelty 7.0 of 10

For small prescribed masses, the m-coupled Gross-Pitaevskii system on a bounded domain in R^3 or R^4 admits arbitrarily many sign-changing and semi-nodal normalized solutions, for all signs of the coupling constants.

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