Mltiple Solutions Of Maxwell Equations With Sublinear Perturbation

In this paper,we consider the nonlinear time-harmonic Maxwell equation? ×(??x?^-1?× E)-V?x?E=???F?x,E?+?·|E|^?-1.E?1.1?in anisotropic bounded medium with sublinear perturbation.where V?x?= ?²??x?.Equation?1.1?is related to the propagation of the time-harmonic electric field in an anisotropic material with a magnetic permeability tensor ?{x)?R^3×3 and a permittiy-ity tensor ??x??R^3×3,? is the rate of the electromagnetic wave.For more physical back grounds one can refer to[1,2,3],etc.The goal of this paper is to find solutions E:??R3 of?1.1?together with the bound?ary condition u × E=0 on?????1.2?where v:?????R³ is the exterior normal.This boundary condition holds when Q is surrounded by a perfect conductor.In this paper,by using the technique of nonlinear functional analysis,we obtain the local minimum of the corresponding functional for the Maxwell equation under sub-linear perturbation.Furthermore,the second solution of the problem,which is different from the local minimum,is obtained by using the method of Thomas Bartsch.