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Dual variational methods for a nonlinear Helmholtz system

Mandel, Rainer; Scheider, Dominic

This paper considers a pair of coupled nonlinear Helmholtz equations on R$^{n}$ where $\frac{2(N+1)}{N−1}$ < $p$ < 2$^{*}$. The existence of nontrivial strong solutions in W$^{2,p}$(R$^{n}$) is established using dual variational methods. The focus lies on necessary and sufficient conditions on the parameters deciding whether or not both components of such solutions are nontrivial.

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DOI: 10.5445/IR/1000075713
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2017
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000075713
Verlag KIT, Karlsruhe
Umfang 24 S.
Serie CRC 1173 ; 2017/25
Schlagworte nonlinear Helmholtz sytem, dual variational methods
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
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