On the existence and uniqueness of limit cycles for generalized Lienard systems

In this paper, we consider a generalized Lienard system dx/dt = phi(y) - F(x), dy/dt = -g(x), where F is continuous and differentiable on an open interval (b(1), a(1)) with -infinity <=, b(1) < 0 < a(1) < +infinity. Assume that there exist a and b with b1 < b < 0 < a < a(1) such that xF(x) < 0 as b < x < a, and xF(x) > 0 as a < x < at or b(1) < x < b. A new uniqueness theorem of limit cycles for the Lienard system (0. 1) is obtained. An example is given to show the application of the theorem. (c) 2008 Elsevier Inc. All rights reserved.