Disconjugacy of complex differential systems

Nonoscillation 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...

Systems-disconjugacy of a Fourth-order Differential Equation1

where r(x) >0 and p(x) are both continuous on [a, oo) and p(x) does not change sign, and related conjugate point properties to oscillation. They gave extensive evidence indicating that the oscillatory behavior when p(x) is positive is essentially different from that when p(x) is negative. Relatively little is known in general when p(x) changes sign or when derivative terms of order less than fo...

K-component Disconjugacy for Systems of Ordinary Differential Equations

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...

Complex fuzzy linear systems