Abstract In this paper, we consider the following nonlinear Maxwell system \ {l@{l} E₁- E₁= H E₂ (x, E₁, E₂) & x \\ E₂- E₂= H E₁ (x, E₁, E₂) & x \\ E₁ =0, ~~~ E₂ =0& x array. ∇ × ∇ × E 1 − λ E 1 = ∂ H ∂ E 2 (x, E 1, E 2) x ∈ Ω ∇ × ∇ × E 2 − λ E 2 = ∂ H ∂ E 1 (x, E 1, E 2) x ∈ Ω ν × E 1 = 0, ν × E 2 = 0 x ∈ ∂ Ω on a bounded domain R^{3 Ω ⊂ R 3 with exterior normal: R^3 ν: ∂ Ω → R 3, E₁ E 1 </mml: ms
Zhang et al. (Mon,) studied this question.