New Ultimate Boundedness and Periodicity Results for Certain Third-order Nonlinear Vector Differential Equations

The principle aim of this paper is to present some new results related to the ultimate boundedness and existence of periodic of solutions a certain non-linear ordinary vector differential equation of third order. Our results improve some well-known results in the literature.</p

Boundedness Results for Solutions of Certain Nonlinear Differential Equations of Second Order

In this paper, we establish some new sufficient conditions which guaranteethe boundedness and the uniform boundedness of solutions of certain nonlinearand nonautonomous differential equations of second order. By defining appropriateLiapunov functions, we obtain some new results on the subject, and examples arealso provided to illustrate the feasibility of the proposed results. By this work, weextend and improve some boundedness results in the literature.DOI : http://dx.doi.org/10.22342/jims.16.2.35.115-12

Stability in Functional Integro-differential Equations of Second Order with Variable Delay

In this paper, we investigate the stability of the zero solution of an integro-differential equation of the second order with variable delay. By means of the fixed point theory and an exponential weighted metric, we find sufficient conditions under which the zero solution of the equation considered is stable

On the instability of nonlinear functional differential equations of fifth order

The author gives sufficient conditions for non-existence of periodic solutions of two higher order nonlinear delay differential systems. Our technical approach is based on the construction of two suitable Lyapunov type functionals. An example is given to illustrate the obtained results. The main results here improve recent results found on the topic in the literature from the case of without delay to the delay case.El autor presenta condiciones suficientes para la existencia de soluciones periódicas de dos ecuaciones diferenciales con retraso de alto orden. El enfoque técnico se fundamenta en la construcción de funcionales de Lyapunov adecuados. Un ejemplo ilustra los resultados obtenidos. El resultado principal presentado en este artículo mejora un resultado reciente en el tema de pasar el caso sin atraso al caso con atraso

Boundedness in third order nonlinear differential equations with bounded delay

A theorem is presented which includes sufficient conditions for the boundedness of solutions of a certain class of third order nonlinear differential equations with a constant delay. Our result extends a recent result by Omeike (2009)