Result on the Convergence Behavior of Solutions of Certain System of Third-Order Nonlinear Differential Equations

Convergence of Solutions of Certain Fourth-Order Nonlinear Differential Equations

We give sufficient criteria for the existence of convergence of solutions for a certain class of fourth-order nonlinear differential equations using Lyapunov's second method. A complete Lyapunov function is employed in this work which makes the results to include and improve some existing results in literature. This is an open access article distributed under the Creative Commons Attribution Li...

On the Asymptotic Behavior of Solutions of Certain Third-order Nonlinear Differential Equations

where ψ ∈ C(R×R×R,R), f ∈ C(R×R,R), and p ∈ C([0,∞)×R×R×R,R). It is also supposed that the functions ψ, f , and p depend only on the arguments displayed explicitly, and the dots denote differentiation with respect to t. However, we shall require that f (0,0) = 0, the derivatives ∂ψ(x, ẋ, ẍ)/∂x ≡ ψx(x, ẋ, ẍ), ∂ψ(x, ẋ, ẍ)/∂ẍ ≡ ψẍ(x, ẋ, ẍ), and ∂ f (x, ẋ)/∂x ≡ fx(x, ẋ) exist and are continuous, an...

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

On the Convergence of Solutions of Certain Third-Order Differential Equations

As well known, in the investigation of qualitative behaviors of solutions, stability, convergence, boundedness, oscillation, and so forth of solutions are very important problems in theory and applications of differential equations. For example, in applied sciences, some practical problems concerning mechanics, the engineering technique fields, economy, control theory, physics, chemistry, biolo...

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.