Abstract: This paper studies the asymptotic behavior of solutions for nonlinear RLC-networks which have the following form
L(i)(di/dt)=(∂P(i,v,t)/∂i)), C(v)(dv/dt)=-(∂P(i,v,t)/∂v).
The function P(i,v,t),called tile mired potential function,call be used to construct Liapunov functions to prove the convergence of solutions under certain conditions. Under the assumption that every element value involving voltage source is asymptotically constant, we establish four creteria for all solutions of such a system to converge to the set of equilibria of its limiting equations via LaSalle invariant principle.We also present two theorems on the existence of periodic solutions for periodically excited nonlinear circuits.This results generalize those of Brayton and Moser^[1,2].

Key words: Nonlinear networks, nonoscillation and oscillation, asymptotic convergence, periodic solutions, LaSalle invariance principle