EXISTENCE AND UNIQUENESS OF CONSTRAINED MINIMIZERS FOR FRACTIONAL KIRCHHOFF TYPE PROBLEMS IN HIGH DIMENSIONS

• DOI: 10.11948/20230311
• Publication Date: 2024-02-05T11:33:28Z
• Authors: Shulin Zhang; ; Hua Jin

In this paper, we investigate the existence and uniqueness of solutions with prescribed $L^{2}$-norm for a class fractional Kirchhoff type problems. Firstly, prove global constraint minimizers exponent $2 < p<2 + \frac{4\theta s}{N}$. Secondly, obtain s}{N}\leq p< 2^{*}_{s}$ by mountain pass theorem. Furthermore, all these are unique up to translations our methods only rely on scaling transformations simply energy estimates. We point out that obtained results extend previous $0<s<1$ $\theta=2$ or $s=1$ in low dimensions. To best knowledge, respect $L^{2}$-subcritical $L^{2}$-critical constrained variational problem problems, critical $p=2 s}{N}$ is properly established first time.