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DOI: 10.5445/IR/1000082023
Veröffentlicht am 13.04.2018

On a fourth order nonlinear Helmholtz equation

Bonheure, Denis; Casteras, Jean-Baptiste; Mandel, Rainer

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.


Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
URN: urn:nbn:de:swb:90-820234
KITopen-ID: 1000082023
Verlag KIT, Karlsruhe
Umfang 21 S.
Serie CRC 1173 ; 2018/3
Schlagworte nonlinear Helmholtz equations, fourth order elliptic equations, dual variational methods
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