Uncountably many solutions for nonlinear Helmholtz and curl-curl equations with general nonlinearities

Abstract

We obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. As an auxiliary tool a Limiting Absorption Principle for the curl-curl operator is proved.

References in corpus (3)

• Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
• Oscillating solutions for nonlinear Helmholtz Equations
• On a fourth order nonlinear Helmholtz equation

Cited by in corpus (2)

• Multiple solutions to a nonlinear curl-curl problem in ${\mathbb{R}}^3$
• Nonlinear curl-curl problems in ${\mathbb{R}}^3$