Oscillation theorems for systems of linear differential equations

Oscillation theorems for systems of linear differential equations

Oscillation of Solutions of Linear Differential Equations

In this note we study the zeros of solutions of differential equations of the form u + pu = 0. A criterion for oscillation is found, and some sharper forms of the Sturm comparison theorem are given. §1. Number of zeros. Consider the linear differential equation u′′(x) + p(x) u(x) = 0 , where p(x) = 1 (1− x) , (1) on the interval −1 < x < 1. Two independent solutions are

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 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...

Oscillation Theorems for Certain Even Order Neutral Differential Equations

This paper is concerned with a class of even order nonlinear differential equations of the form d dt “ ̨