Existence and uniqueness of normalized solutions for the Kirchhoff equation

For a class of Kirchhoff functional, we first give a complete classification with respect to the exponent p for its L2-normalized critical points, and show that the minimizer of the functional, if exists, is unique up to translations. Secondly, we search for the mountain pass type critical points fo...

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Bibliographic Details
Published in:Applied mathematics letters 2017-12, Vol.74, p.52-59
Main Authors: Zeng, Xiaoyu, Zhang, Yimin
Format: Article
Language:English
Subjects:
[formula omitted]-normalized critical point
Kirchhoff equation
Uniqueness
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Summary:For a class of Kirchhoff functional, we first give a complete classification with respect to the exponent p for its L2-normalized critical points, and show that the minimizer of the functional, if exists, is unique up to translations. Secondly, we search for the mountain pass type critical points for the functional on the L2-normalized manifold, and also prove that this type critical point is unique up to translations. Our proof relies only on some simple energy estimates and avoids using the concentration-compactness principles. These conclusions extend some known results in previous papers.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2017.05.012