Journal ArticleDOI
A note on an inequality similar to lyapunov's inequality
TLDR
In this article, it is assumed that solutions of (3) and also of some generalizations of the form (3), both of which are real-valued and continuous on I.Abstract:
(3) (\\y'(t)\\~y'{t))' + q(t)\\y(t)ry(t) = o , P > 1 , where / € / = [0, and I contains the points a,b (a < b), the function q is real-valued and continuous on I . The problems of existence, uniqueness and other properties of solutions to equations of the form (3) are recently studied in [3]-[5]. In what follows it is assumed that solutions of (3), and also of some generalizations of (3), exist on I .read more
Citations
More filters
Journal ArticleDOI
New gaps between zeros of fourth-order differential equations via Opial inequalities
TL;DR: In this paper, for a fourth-order differential equation, the authors established lower bounds for the distance between zeros of a nontrivial solution and their derivatives, and for the boundary value problems in the theory of bending of beams.
Journal ArticleDOI
On the Behavior of Some Second Order Nonlinear Differential Equations
TL;DR: In this paper, the authors studied the second order nonlinear differential equations of type y″+p(t)y+q(t),f(y) = 0, including properties such as positivity, number of zeros, oscillating nature, boundedness and monotonicity of the solutions.
References
More filters
Journal ArticleDOI
A Lyapunov inequality and forced oscillations in general nonlinear nth order differential-difference equations†
TL;DR: In this article, an inequality of Lyapunov type was derived to find conditions to ensure that the oscillatory solutions of equation (1) tend to zero as t → ∞.
Journal ArticleDOI
On an inequality of Lyapunov for disfocality
TL;DR: The authors renforce l'inegalite de Lyapunov d'une autre maniere, toujours en utilisant la disfocalite, basee sur une decomposition d'intervalle.