An extension of the Lienard theorem and its application [nonlinear circuits]

The authors present a theorem asserting the existence of a unique stable periodic solution of the differential equation d² x/dt²+f(x)dx /dt+ g(x)=0 under the same conditions as those of the well-known Lienard theorem, except for the condition for f(x) and g(x) in the Lienard theorem replaced by the condition that they are respectively not necessarily even and odd with respect to x. Also, as a simple illustrative example, the extended theorem is applied to an oscillator circuit consisting of L, C, R, a tunnel diode, and a battery. A criterion of the existence of stable oscillation is given with respect to the range of a DC bias