A general RLC system with complex values

Abstract

We study a semilinear second-order ordinary differential equation for a complex valued function Q which describes the evolution of a generalized RLC system over an interval [0, T ]. We solve the Dirichlet and periodic problems under appropriate conditions. Moreover, we give conditions in order to ensure that any solution satisfying an initial condition Q(0) = Q 0, Q′(0)= I 0 is defined over [0, T ].