Stability and boundedness properties of solutions to certain fifth order nonlinear differential equations

Abstract

In this paper, we consider the nonlinear fifthorder differential equation$$x^{(v)}+a{x}^{(iv)}+b\stackrel{⃛}{x}+f(\ddot{x})+g(\dot{x})+h(x)=p(t;x,\dot{x},\ddot{x},\stackrel{⃛}{x},x^{(iv)})$$ and we used theLyapunov's second method to give sufficient criteria for the zerosolution to be globally asymptotically stable as well as theuniform boundedness of all solutions with their derivatives.