Journal
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
Volume 19, Issue 1, Pages 959-986Publisher
SPRINGER BASEL AG
DOI: 10.1007/s11784-017-0409-1
Keywords
Time-harmonic Maxwell equations; perfect conductor; anisotropic media; uniaxial media; nonlinear material; ground state; variational methods; strongly indefinite functional; Nehari-Pankov manifold
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Funding
- National Science Centre, Poland [2014/15/D/ST1/03638]
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The search for time-harmonic solutions of nonlinear Maxwell equations in the absence of charges and currents leads to the elliptic equation for the field in a domain . Here, is the (linear) permittivity tensor of the material, and denotes the magnetic permeability tensor. The nonlinearity comes from the nonlinear polarization. If is a gradient, then this equation has a variational structure. The goal of this paper is to give an introduction to the problem and the variational approach, and to survey recent results on ground and bound state solutions. It also contains refinements of known results and some new results.
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