Disconjugacy conditions for linear third-order differential equations
نویسندگان
چکیده
منابع مشابه
Criteria for Disfocality and Disconjugacy for Third Order Differential Equations∗
In this paper, lower bounds for the spacing (b− a) of the zeros of the solutions and the zeros of the derivative of the solutions of third order differential equations of the form y + q(t)y + p(t)y = 0 (∗) are derived under the some assumptions on p and q. The concept of disfocality is introduced for third order differential equations (*). This helps to improve the Liapunov-type inequality, whe...
متن کاملApproximately $n$-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.
متن کاملLyapunov-type Inequalities for Third-order Linear Differential Equations
In this article, we establish new Lyapunov-type inequalities for third-order linear differential equations y′′′ + q(t)y = 0 under the three-point boundary conditions y(a) = y(b) = y(c) = 0 and y(a) = y′′(d) = y(b) = 0 by bounding Green’s functions G(t, s) corresponding to appropriate boundary conditions. Thus, we obtain the best constants of Lyapunov-type inequalities for three-point boundary v...
متن کاملLyapunov–type Inequalities for Third–order Linear Differential Equations
In this paper, we obtain new Lyapunov-type inequalities for the third-order linear differential equation x′′′ + q(t)x = 0 . Our work provides the sharpest results in the literature and makes corrections to those in a recently published paper [1]. Based on the above, we further establish new Lyapunov-type inequalities for more general third-order linear differential equations. Moreover, by combi...
متن کاملNonoscillation and disconjugacy of systems of linear differential equations
The differential equations under consideration are of the form (1) §f = A(t)x, where A(t) is a piecewise continuous real nxn-matrix on a real interval a, and the vector x = (x-j...,x ) is continuous on a. The equation is said to be nonoscillatory on a if every nontrivial real solution vector x has at least one component xv which does not vanish on a. The principal concern of this paper is the d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1968
ISSN: 0022-0396
DOI: 10.1016/0022-0396(68)90023-5