Dual variational methods for static Nonlinear Maxwell's Equations

Rainer Mandel

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arXiv · 2109.00826

Dual variational methods for static Nonlinear Maxwell's Equations

Rainer Mandel

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Abstract

We prove the existence of a ground state and infinitely many geometrically distinct solutions for static nonlinear Maxwell's equations on $\mathbb{R}^3$. Our existence result relies on a variant of the Symmetric Mountain Pass Theorem that applies to periodic as well as vanishing nonlinearities. It is applied in a dual variational setting and thus provides an alternative approach with respect to the direct variational method introduced by Mederski.

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Rainer Mandel. 2021-09-02. Dual variational methods for static Nonlinear Maxwell's Equations. https://arxiv.org/abs/2109.00826

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