Communications in Mathematical Physics

, Volume 368, Issue 2, pp 799–842 | Cite as

The Limiting Absorption Principle for Periodic Differential Operators and Applications to Nonlinear Helmholtz Equations

  • Rainer MandelEmail author


We prove an Lp-version of the limiting absorption principle for a class of periodic elliptic differential operators of second order. The result is applied to the construction of nontrivial solutions of nonlinear Helmholtz equations with periodic coefficient functions.


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The author thanks the reviewer for several helpful remarks and corrections. Furthermore, he is grateful to TomášDohnal (Martin-Luther-UniversitätHalle-Wittenberg) for stimulating discussions about Floquet-Bloch theory during the past years and for providing Fig. 1. Additionally, he gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173 ”Wave phenomena: analysis and numerics”.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Karlsruhe Institute of TechnologyInstitute for AnalysisKarlsruheGermany

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