Nondegeneracy of ground states for nonlinear scalar field equations involving the Sobolev-critical exponent at high frequencies in three and four dimensions
| Autor: | Akahori, Takafumi, Murata, Miho |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider nonlinear scalar field equations involving the Sobolev-critical exponent at high frequencies $\omega$. Since the limiting profile of the ground state as $\omega \to \infty$ is the Aubin-Talenti function and degenerate in a certain sense, from the point of view of perturbation methods, the nondegeneracy problem for the ground states at high frequencies is subtle. In addition, since the limiting profile (Aubin-Talenti function) fails to lie in $L^{2}(\mathbb{R}^{d})$ for $d=3,4$, the nondegeneracy problem for $d=3,4$ is more difficult than that for $d\ge 5$ and an applicable methodology is not known. In this paper, we solve the nondegeneracy problem for $d=3,4$ by modifying the arguments in [2, 3]. We also show that the linearized operator around the ground state has exactly one negative eigenvalue. Comment: 35 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|