Time‐harmonic and asymptotically linear Maxwell equations in anisotropic media

Abstract

This paper is focused on following time‐harmonic Maxwell equation: urn:x-wiley:mma:media:mma4615:mma4615-math-0001 where is a bounded Lipschitz domain, is the exterior normal, and ω is the frequency. The boundary condition holds when Ω is surrounded by a perfect conductor. Assuming that f is asymptotically linear as , we study the above equation by improving the generalized Nehari manifold method. For an anisotropic material with magnetic permeability tensor and permittivity tensor , ground state solutions are established in this paper. Applying the principle of symmetric criticality, we find 2 types of solutions with cylindrical symmetries in particular for the uniaxial material.