Ground States of Time-Harmonic Semilinear Maxwell Equations in $${\mathbb{R}^3}$$ R 3 with Vanishing Permittivity
Ground States of Time-Harmonic Semilinear Maxwell Equations in $${\mathbb{R}^3}$$ R 3 with Vanishing Permittivity
We investigate the existence of solutions $${E:\mathbb{R}^3 \to \mathbb{R}^3}$$ of the time-harmonic semilinear Maxwell equation $$\nabla \times (\nabla \times E) + V(x) E = \partial_E F(x, E) \quad {\rm in} \mathbb{R}^3$$ where $${V:\mathbb{R}^3 \to \mathbb{R}}$$ , $${V(x) \leqq 0}$$ almost everywhere on $${\mathbb{R}^3}$$ , $${\nabla \times}$$ denotes the curl operator …