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On a fourth order nonlinear Helmholtz equation

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

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.

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DOI: 10.5445/IR/1000082023
Veröffentlicht am 13.04.2018
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
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
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
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