Oscillating solutions for nonlinear Helmholtz Equations
Analysis of PDEs
2017-10-25 v1
Abstract
Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behavior 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 Schr\"odinger equations with large frequencies.
Cite
@article{arxiv.1702.03727,
title = {Oscillating solutions for nonlinear Helmholtz Equations},
author = {Rainer Mandel and Eugenio Montefusco and Benedetta Pellacci},
journal= {arXiv preprint arXiv:1702.03727},
year = {2017}
}