Search

In this paper, asymptotic stability and global asymptotic stability of solutions to a deterministic and compartmental mathematical model of measles infection is considered using the ideas of the Jacobian determinant as well as the second method of Lyapunov, criteria/conditions that guaranteed asymptotic stability of disease free equilibrium and endemic equilibrium were established. Also the basic reproductive number R0 was obtained. The results in this work compliments existing work and provided further information in controlling the disease in an open population. [ABSTRACT FROM AUTHOR]

In this paper, some new conditions on the global asymptotic stability, boundedness and ultimate boundedness of solutions to a certain fourth order nonlinear differential equation are obtained. By constructing a complete Lyapunov function, we give three new results on the considered equation. Our results improve, generalize and complement existing results in the literature on the subject matter. [ABSTRACT FROM AUTHOR]

This paper is concerned with the convergence of solutions to the fourth order nonlinear differential equation x(iv) + φ(x⃛ + f(ẍ) + g(ẋ) + h(x) = p(t, x, ẋ, ẍ, x⃛ where the nonlinear functions φ f; g; h and p are continuous. By constructing a complete Lyapunov function, some fundamental questions on whether convergence results on the above equation which do not appear to have received any attention in the literature can be proved, are answered. [ABSTRACT FROM AUTHOR]