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Demonstrates the existence of infinitely many solutions in a nonlinear Maxwell system, suggesting significant implications for electromagnetic theory.
In this paper, we consider the following nonlinear Maxwell system \ arrayl@l ∇ × ∇ × E₁-λ E₁= ∂ H∂ E₂(x,E₁,E₂) &x∈ Ω \\ ∇ × ∇ × E₂-λ E₂= ∂ H∂ E₁(x,E₁,E₂) &x∈ Ω \\ ν × E₁ =0,~~~ ν × E₂ =0&x∈ ∂ Ω 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 Ω ⊂ R³ Ω ⊂ R 3 with exterior normal ν :∂ Ω → R³ ν : ∂ Ω → R 3 , E₁ E 1 </mml:ms
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Zhang et al. (2026) studied this question.
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