Asymptotic representations of solutions of the nonautonomous ordinary differential $n$-th order equations

Positive solutions of boundary value problems for n th order ordinary differential equations 1 Moustafa

In this paper, we investigate the problem of existence and nonexistence of positive solutions for the nonlinear boundary value problem: u(t) + λa(t)f(u(t)) = 0, 0 < t < 1, satisfying three kinds of different boundary value conditions. Our analysis relies on Krasnoselskii’s fixed point theorem of cone. An example is also given to illustrate the main results.

ASYMPTOTIC BEHAVIOUR OF OSCILLATORY SOLUTIONS OF n - TH ORDER DIFFERENTIAL EQUATIONS

In this paper, sufficient conditions have been obtained so that all oscillatory solutions of the n-th order differential equations with quasi derivatives tend to zero as t tends to infinity.

ASYMPTOTIC BEHAVIOUR OF SOLUTIONS TO n-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

We establish conditions for the linear differential equation y(t) + p(t)y(g(t)) = 0 to have property A. Explicit sufficient conditions for the oscillation of the the equation is obtained while dealing with the property A of the equations. A comparison theorem is obtained for the oscillation of the equation with the oscillation of a third order ordinary differential equation.

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...