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 ) : x ″ ( t ) + f 1 ( x ( t ) , x ( t − r ( t ) ) , x ′ ( t ) , x ′ ( t − r ( t ) ) ) x ′ ( t ) + f 2 ( x ( t ) , x ( t − r ( t ) ) , x ′ ( t ) , x ′ ( t − r ( t ) ) ) ( x ′ ( t ) ) 2 + g 1 ( x ( t ) ) + g 2 ( 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.