Rectifiable oscillations in second-order linear differential equations

Two–point Oscillations in Second–order Linear Differential Equations

A second-order linear differential equation (P) : y′′ + f (x)y = 0 , x ∈ I , where I = (0,1) and f ∈ C(I) , is said to be two-point oscillatory on I , if all its nontrivial solutions y ∈ C( I )∩C2(I) , oscillate both at x = 0 and x = 1 , i.e. having sequences of infinite zeros converging to x = 0 and x = 1 . It necessarily implies that all solutions y(x) of (P) must satisfy the Dirichlet bounda...

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

Second Order Linear and Nonlinear Differential Equations'

Approximately $n$-order linear differential equations

We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

Recurrent metrics in the geometry of second order differential equations

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...