On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument

This paper investigates stability and boundedness of solutions to third order nonlinear differential equation with retarded argument: $$begin{array}{l}x'''(t)+varphibigl(x(t-r),x'(t-r),x''(t-r)bigr)x''(t)qquad{}+psibigl(x'(t-r)bigr)+hbigl(x(t-r)bigr)quad=pbigl(t,x(t),x(t-r),x'(t),x'(t-r),x''(t)bigr).end{array}$$ By the use of the Lyapunov functional, sufficient conditions for stability and boundedness of solutions to the considered equations are obtained. Examples are introduced throughout the paper for illustrations.