Abstract
The paper is concerned about the existence of solutions with prescribed -norm to the following Kirchhoff-type equation where or , . Noting that 14/3 is the mass critical exponent, a Pohozaev constraint method is adopted in two cases. In the mass mixed critical case, i.e., , we get a normalized solution to above equation with small enough μ by Ekeland's variational principle. In the mass supercritical case, i.e., , we obtain a positive ground state normalized solution, and energy comparison argument is used in the Sobolev critical case.
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Acknowledgments
The author would like to thank the reviewers for careful reading and valuable suggestions.
Disclosure statement
No potential conflict of interest was reported by the author.