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<p>We prove the existence of infinitely many nontrivial solutions for time-harmonic nonlinear Maxwell’s equations on bounded domains and on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> 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.</p>

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Dual variational methods for time-harmonic nonlinear Maxwell’s equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月18日

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  • Rainer Mandel

摘要

We prove the existence of infinitely many nontrivial solutions for time-harmonic nonlinear Maxwell’s equations on bounded domains and on \(\mathbb {R}^3\) R 3 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.