CONVERGENCE BEHAVIOR OF SOLUTIONS OF A KIND OF THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS
Convergent behavior of solutions as well as critical variables characterizing the systems of nonlinear differential equations is very important. Convergence or extreme stability of solutions of third order differential equations in applied mathematics is specified by physical nature of their function. Convergence of solutions of third order differential equations where the nonlinear term is not a function of x and alone is quite rare. In this paper, we consider a problem related to the convergence behavior of such a system. Analysis is carried out using Lyapunov’s second or direct method to obtain sufficient conditions which ensure that the solutions of the system considered are convergent. For illustration, examples are given on the convergent solutions.
convergence of solutions, third order nonlinear differential equations, Lyapunov functional.