Systems-disconjugacy of a fourth-order differential equations

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...

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...

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...

K-component Disconjugacy for Systems of Ordinary Differential Equations

Numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...