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Oscillating solutions for nonlinear Helmholtz equations

  • Rainer Mandel
  • Eugenio Montefusco
  • Benedetta Pellacci
Article

Abstract

Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behaviour at infinity is established. Some generalizations to nonautonomous radial equations as well as existence results for nonradial solutions are found. Our theorems prove the existence of standing waves solutions of nonlinear Klein–Gordon or Schrödinger equations with large frequencies.

Keywords

Nonlinear Helmholtz equations Standing waves Oscillating solutions 

Mathematics Subject Classification

35J05 35J20 35Q55 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut für AnalysisKarlsruher Institut für TechnologieKarlsruheGermany
  2. 2.Dipartimento di Matematica”Sapienza” Università di RomaRomeItaly
  3. 3.Dipartimento di Scienze e TecnologieUniversità di Napoli ”Parthenope”NaplesItaly

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