Oscillation and asymptotic properties of $n$-th order differential equations

Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations

Oscillation and asymptotic properties of a class of second-order Emden–Fowler neutral differential equations

We consider a class of second-order Emden-Fowler equations with positive and nonpositve neutral coefficients. By using the Riccati transformation and inequalities, several oscillation and asymptotic results are established. Some examples are given to illustrate the main results.

An existence result for n^{th}-order nonlinear fractional differential equations

In this paper, we investigate the existence of solutions of some three-point boundary value problems for n-th order nonlinear fractional differential equations with higher boundary conditions by using a fixed point theorem on cones.

Asymptotic behavior of n-th order dynamic equations

We are concerned with the asymptotic behavior of solutions of an nth order linear dynamic equation on a time scale in terms of Taylor monomials. In particular, we describe the asymptotic behavior of the so-called (first) principal solution in terms of the Taylor monomial of degree n−1. Several interesting properties of the Taylor monomials are established so that we can prove our main results.

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.