On the stability and ultimate boundedness of solutions for certain third order differential equations

Abstract

With respect to our observation in the relevant literature, work on stability and boundedness of solution for certain third order nonlinear differential equations where the nonlinear and the forcing terms depend on certain variables are scare. The objective of this study was to get criteria for stability and boundedness of solutions for these classes of differential equations. Approach: Using Lyapunov second or direct method, a complete Lyapunov function was constructed and used to obtain our results. Results: Conditions were obtained for: (i) Uniform asymptotic stability and, (ii) Uniform ultimate boundedness, of solutions for certain third order non-linear non-autonomous differential equations. Conclusion: Our results do not only bridge the gap but extend some well-known results in the literature.