On a fourth order nonlinear Helmholtz equation
Abstract:
In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation Δ²u − βΔu + αu = Γ|u|$^{p-2}$u in R$^{N}$, for positive, bounded and Z$^{N}$-periodic functions Γ in the following three cases:
(a) α < 0, β E R or (b) α > 0, β < −2√α or (c) α = 0, β < 0. Using the dual method of Evéquoz and Weth, we find solutions to this equation and establish some of their qualitative properties.
(a) α < 0, β E R or (b) α > 0, β < −2√α or (c) α = 0, β < 0. Using the dual method of Evéquoz and Weth, we find solutions to this equation and establish some of their qualitative properties.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsjahr | 2018 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X urn:nbn:de:swb:90-820234 KITopen-ID: 1000082023 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 21 S. |
| Serie | CRC 1173 ; 2018/3 |
| Schlagwörter | nonlinear Helmholtz equations, fourth order elliptic equations, dual variational methods |