Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl Equations
Rainer Mandel · Advanced Nonlinear Studies · 2019
Abstract We obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. The constructed solutions are mildly localized as they lie in the essential spectrum of the corresponding linear operator. As a new auxiliary tool a limiting absorption principle for the curl-curl operator is proved.