On A Matrix Hypergeometric Differential Equation

In this paper, we study the growth of solutions of the second order linear complex differential equations insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .

In this paper, we apply a new procedure initially developed in Refs. [H. El-Owaidy and H.Y. Mohamed. "On the periodic solutions for nth order difference equations". Journal of Applied Mathematics and Computation , (to appear); "The necessary and sufficient conditions of existence of periodic solutions of nonautonomous difference equations". Journal of Applied Mathematics and Computation , (to appear)] to simplify the use of Carvalho's method to the case of discrete difference equations, in order to find the periodic solutions of second order linear difference equations. We can also find the complex periodic solutions.

Taylor polynomial solutions of second order linear partial differential equations

(1970). A Representation Formula for the Solutions of the Second Order Linear Differential Equation. Mathematics Magazine: Vol. 43, No. 2, pp. 77-80.

In this paper, we propose a variational-fixed point iteration technique for the solution of second order linear differential equations with two-point boundary value problems. The proposed method is endowed with the Galerkin method for the determination of the starting function. The numerical results show the validity and efficiency of the proposed method in comparison withthe exact solution and other existing methods. Keywords: Variational iteration method, Galerkin method, Fixed point iteration method, Differential equation

Here, first we shall set together various basic statements on the periodicity of the solutions of first order linear difference equations, then we shall define various discrete functions which are in a sense connected with the concept of periodicity. Finally, we will formulate a decomposition theorem for the solutions of first order linear difference equations with periodic coefficients.

Improving explicit bounds for the solutions of second order linear differential equations

Zeros of solutions of certain second order linear differential equation

An integro-iteration method is applied to solve the second order linear differential equation. Although the procedure is quite elementary it produces the general solution in form of a simple series which can be made to converge absolutely, at least in the region of interest. Particular solutions with given initial or boundary values can be readily obtained from the general solution.

SynopsisLetddenote the dimension of the vector space consisting of all solutions of the equation − (p(t)y′)′ +q(t)y= 0,a≤t< ∞; that lie in the function spaceL2[a, ∞). By means of certain bounds on the solutions of this equation, sufficiency criteria are obtained for the casesd= 0 andd= 2.

SECTION 6 - Solutions of Linear Equations

Instability of solution for a class of the third order nonlinear differential equation

Let L be a second order differential equation with coefficients in C(x). The goal of this paper is to find solutions of L in the form exp(∫r dx#8226;2; F1(a1a2b1; f)(1) where r; f E Q(x), and a1; a2; b1 EQ.

The present paper deals with special solutions for linear functional differential equations with small delays. The importance of special solutions relies on the fact that, under some conditions, they can be used to describe the asymptotic behaviour of all solutions. Sufficient conditions for the existence of special solutions for nonautonomous equations in $\mathbb R^n$ are given. For autonomous equations in $\mathbb R^n$, results relating special solutions and characteristic values are presented. We also consider linear autonomous functional differential equations in Banach spaces, and use special solutions to study the asymptotic behaviour of their solutions. Several applications are given.

In this paper, we present conditions ensuring that solutions of linear second-order differential equations oscillate, provided solutions of corresponding difference equations oscillate. We also establish the converse result, namely, when oscillation of solutions of difference equations implies oscillation of solutions of corresponding differential equations.