Theorems of oscillation for two linear differential equations of the second order with two parameters

Oscillation Theorems for Second Order Nonlinear Differential Equations with Damping

Some oscillation criteria for solutions of a general ordinary differential equation of second order of the form (r(t)ψ(x(t))ẋ(t))+h(t)ẋ(t)+q(t)φ(g(x(t)),r(t)ψ(x(t))ẋ(t)) = H(t,x(t), ẋ(t)) with alternating coefficients are discussed. Our results improve and extend some existing results in the literature. Some illustrative examples are given with its numerical solutions which are computed using R...

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Oscillation theorems for second order neutral differential equations

In this paper new oscillation criteria for the second order neutral differential equations of the form (E) ` r(t) [x(t) + p(t)x(τ (t))]′ ́ ′ + q(t)x(σ(t)) + v(t)x(η(t)) = 0 are presented. Gained results are based on the new comparison theorems, that enable us to reduce the problem of the oscillation of the second order equation to the oscillation of the first order equation. Obtained comparison ...

Oscillation Theorems for Second Order Advanced Neutral Differential Equations

The aim of this paper is to study the oscillation of the second order advanced neutral differential equations r(t) x(t) + p(t)x τ (t) ′ ′ + q(t)x σ(t) = 0. (E) Obtained results are based on the new comparison theorems that enable us to reduce problem of the oscillation of the second order equation to the the oscillation of the first order equations. Obtained comparison principles essentially si...