Analysis proves infinitely many solutions for nonlinear maxwell's equations, indicating dual variational approaches are effective.
We prove the existence of infinitely many nontrivial solutions for time-harmonic nonlinear Maxwell's equations on bounded domains and on R³ using dual variational methods. In the dual setting we apply a new version of the Symmetric Mountain Pass Theorem that does not require the Palais-Smale condition.
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Rainer Mandel (2025) studied this question.
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