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.

Oscillating solutions for nonlinear Helmholtz equations / Mandel, Rainer; Montefusco, Eugenio; Benedetta, Pelacci. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - STAMPA. - 68:(2017). [10.1007/s00033-017-0859-8]

Oscillating solutions for nonlinear Helmholtz equations

MANDEL, RAINER;Eugenio Montefusco;
2017

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.
2017
nonlinear Helmholtz equations; standing waves; oscillating solutions
01 Pubblicazione su rivista::01a Articolo in rivista
Oscillating solutions for nonlinear Helmholtz equations / Mandel, Rainer; Montefusco, Eugenio; Benedetta, Pelacci. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - STAMPA. - 68:(2017). [10.1007/s00033-017-0859-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1028799
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