Cemil Tunç: Instability of solutions of vector Liénard equation with constant delay, p.197-204

Abstract:

We consider the vector Liénard equation with the constant delay $\tau >0$,$$X^{\prime \prime }(t)+F(X(t),X^{\prime }(t))X^{\prime }(t)+H(X(t-\tau ))=0.$$ We establish certain sufficient conditions, which guarantee the instability of the zero solution of this equation. An example is given to illustrate the theoretical analysis in this work.

Key Words: Vector Liénard equation, instability, delay.

2000 Mathematics Subject Classification: Primary: 34K12;
Secondary: 34K20.