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.| File | Dimensione | Formato | |
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