Some new stability and boundedness results of solutions of Liénard type equations with a deviating argument

This paper concerns the stability and boundedness of solutions to the following Liénard type equation with a variable deviating argument, r(t)r(t): x″(t)+f1(x(t),x(t−r(t)),x′(t),x′(t−r(t)))x′(t)+f2(x(t),x(t−r(t)),x′(t),x′(t−r(t)))(x′(t))2+g1(x(t))+g2(x(t−r(t)))=p(t,x(t),x(t−r(t)),x′(t),x′(t−r(t))).x″(t)+f1(x(t),x(t−r(t)),x′(t),x′(t−r(t)))x′(t)+f2(x(t),x(t−r(t)),x′(t),x′(t−r(t)))(x′(t))2+g1(x(t))+g2(x(t−r(t)))=p(t,x(t),x(t−r(t)),x′(t),x′(t−r(t))). By means of the Lyapunov second (direct) method, we obtain two new results on the subject and give an example for the illustration of the topic.