Lyapunov's second method for nonautonomous differential equations

Lyapunov’s Second Method for Nonautonomous Differential Equations

Converse Lyapunov theorems are presented for nonautonomous systems modelled as skew product flows. These characterize various types of stability of invariant sets and pullback, forward and uniform attractors in such nonautonomous systems. MSC subject classification: 37B25, 37B55, 93D30

Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations

Periodic Solutions of Second-order Nonautonomous Impulsive Differential Equations

The main purpose of this paper is to study the existence of periodic solutions of second order impulsive differential equations with superlinear nonlinear terms. Our result generalizes one of Paul H. Rabinowitz’s existence results of periodic solutions of second order ordinary differential equations to impulsive cases. Mountain Pass Lemma is applied in order to prove our main results. AMS Subje...

Modified Laplace Decomposition Method for Singular IVPs in the second-Order Ordinary Differential Equations

  In this paper, we use modified Laplace decomposition method to solving initial value problems (IVP) of the second order ordinary differential equations. Theproposed method can be applied to linear and nonlinearproblems    

A NEW MODIFIED HOMOTOPY PERTURBATION METHOD FOR SOLVING LINEAR SECOND-ORDER FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm type Integro-differential equations using a new method which is based on Improved homotopy perturbation method (IHPM) and applying accelerating parameters. This method is very simple and the result is obtained very fast.