We study global solutions to a fourth order semilinear ordinary differential equation. We determine sufficient conditions on the nonlinearity that ensure global continuation of the solutions. Furthermore, we discuss their qualitative behaviors such as oscillations and boundedness. Mathematics Subject Classification: 34C11, 34A12.

Let G and f : [0,1]×R4 → R be two functions satisfying Caratheodory conditions. This paper is concerned with the problems of existence and uniqueness of solutions for the nonlinear fourth-order ordinary differential equation y′′′′ +λy′′ +ky+G(x,y,y′,y′′,y′′′)= f (x,y,y′,y′′,y′′′) with one of a particular set of boundary conditions.

Uniqueness implies uniqueness relationships are examined among solutions of the fourth-order ordinary differential equation, y (4) = f (x, y, y , y , y), satisfying 5-point, 4-point, and 3-point nonlocal boundary conditions. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution , and reproduction in any medium, pr...

We give criteria for the asymptotic stability and boundedness of solutions to the nonlinear fourth-order ordinary differential equation x + φ(ẍ) ... x + f(x, ẋ)ẍ + g(ẋ) + h(x) = p(t, x, ẋ, ẍ, ... x ) , when p ≡ 0 and when p 6= 0. Our results include and improve some well-known results in the literature.

In this paper we investigate the existence of solutions of a class of four-point boundary value problems for a fourth order ordinary differential equation. Our analysis relies on a nonlinear alternative of Leray–Schauder type. c © 2007 Elsevier Ltd. All rights reserved.

We present here the solution of the problem on linearization of fourthorder equations by means of point transformations. We show that all fourth-order equations that are linearizable by point transformations are contained in the class of equations which is linear in the third-order derivative. We provide the linearization test and describe the procedure for obtaining the linearizing transformat...