Multiple cylindrically symmetric solutions of nonlinear Maxwell equations - Wen, Yanyun; Zhao, Peihao (Topological Methods in Nonlinear Analysis, 2023)
In this paper, we study the following nonlinear time-harmonic Maxwell equations equationequation 0.1 abla×( abla × E)-ω^2ε(x)E =P(x)|E|^p-2E+Q(x)|E|^q-2E, equation where ε(x) is the permittivity of the material, xR^3, 1< q< p/(p-1)< 2< p< 6, P(x),Q(x)C(R^3,R). Under some special cylindrical symmetric conditions for ε(x), P(x) and Q(x), we obtain infinite many cylindrically symmetric solutions of equation 0.1 by using variational method and fountain theorems without τ-upper semi-continuity.