Effect of nonlinear perturbations on second order linear nonoscillatory differential equations
نویسندگان
چکیده
Abstract. The aim of this paper is to show that any second order nonoscillatory linear differential equation can be converted into an oscillating system by applying a “sufficiently large”nonlinear perturbation. This can be achieved through a detailed analysis of possible nonoscillatory solutions of the perturbed differential equation which may exist when the perturbation is “sufficiently small”. As a consequence the class of oscillation-generating perturbations is determined precisely with respect to the original nonoscillatory linear equation.
منابع مشابه
Basic results on distributed order fractional hybrid differential equations with linear perturbations
In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...
متن کاملOn 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
متن کاملClassification of Nonoscillatory Solutions of Nonlinear Neutral Differential Equations
Nonoscillatory solutions of a general class of second order functional neutral differential equations of the form
متن کاملAn Asymptotic Formula for Solutions of Nonoscillatory Half-linear Differential Equations
We establish a Hartman type asymptotic formula for nonoscillatory solutions of the half-linear second order differential equation ( r(t)Φ(y′) )′ + c(t)Φ(y) = 0 , Φ(y) := |y|p−2y , p > 1 .
متن کاملOscillation and Asymptotic Behaviour of Solutions of Second Order Neutral Differential Equations with Positive and Negative Coefficients
Sufficient conditions in terms of the coefficient functions for the oscillation and asymptotic behavior of nonoscillatory solutions of a class of second order nonlinear neutral differential equations have been obtained. The results improve some earlier results.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010