Dual variational methods for an indefinte nonlinear Helmholtz equation
Abstract:
We prove new existence results for a Nonlinear Helmholtz equation with sign-changing nonlinearity of the form $$-\Delta u-k^2u=Q(x)|u|^{p-2}u,\quad u\in W^{2,p}(\mathbb{R}^N)$$ with $k>0, N\ge3,p\in\left[\frac{2(N+1)}{N-1},\frac{2N}{N-2}\right]$ and $Q\in L^\infty(\mathbb{R}^N)$. Due to sign-changes of $Q$, our solutions have infinite Morse-Index in the
corresponding dual variational formulation.
corresponding dual variational formulation.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsmonat/-jahr | 11.2020 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000126434 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 17 S. |
| Serie | CRC 1173 Preprint ; 2020/35 |
| Projektinformation | SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) |
| Externe Relationen | Siehe auch |
| Schlagwörter | indefinite variational problem, dual variational method, nonlinear Helmholtz equation, saddle-point reduction |