Abstract: “The present paper is devoted to the investigation of lossless transmission lines with time-varying specific parameters terminated by nonlinear conductive loads with interval of negative conductance. We give a general method for reducing the mixed problem for the arising hyperbolic system to an initial value problem for neutral system on the boundary. Here we overcome difficulties arising from time-varying specific parameters and formulate conditions for the existence of oscillatory solutions.”

Keywords: transmission lines with time-varying specific parameters, oscillatory solutions, nonlinear boundary value problem, fixed point theorem.