JMAT_V1_N4_RP1 Vasil Angelov Dafinka Angelova Journal on Mathematics 2277-5137 1 4 22 33 Lossy Transmission Lines, Oscillatory Solutions, Neutral Equations, Fixed Point Theorem This present paper is devoted to investigation of lossy transmissions lines terminated by a nonlinear resistive element. The transmission line is terminated by an R-element with exponential nonlinearity in the V-I characteristic. The reducing of the mixed problem for Telegrapher hyperbolic system to an initial value problem for a nonlinear neutral equation on the boundary is made in [3]. The nonlinearity in the boundary condition is transferred to the neutral equation on the boundary. Then we introduce a suitable operator whose fixed point is an oscillatory solution of the neutral equation. The main existence-uniqueness theorem contains conditions which guarantee that the operator mentioned is contractive one in a uniform space. Finally, we demonstrate how to apply the results obtained to the circuit design. October - December 2012 Copyright © 2012 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=2047