Order Matrix Differential Equations Research Articles

Oscillation criteria for nonlinear second order matrix differential equations

The object of this paper is to present sufficient conditions for the oscillation of certain solutions of the second order, nonlinear matrix differential equation. The oscillation criteria obtained here improve the recent results of the author and E. C. Tomastik. The methods employed in the paper extend a technique introduced by H. C. Howard and for the special linear version of the nonlinear equation, the resulting oscillation criteria represent improvement of Howard’s work. Using an extension of the unitary transformation introduced by F. V. Atkinson, estimates of the oscillation of solutions are obtained.

Oscillation Criteria for Nonlinear Second Order Matrix Differential Equations

Oscillation Criteria for Nonlinear Second Order Matrix Differential Equations

The Semi-Infinite Elastic Cylinder Under Self-Equilibrated End Loading

This paper presents a practical formulation for the solution of the elastostatic problem of a semi-infinite solid cylinder with the long sides free from stress and self-equilibrated tractions applied on the end. The formulation is entirely in terms of stresses and displacement related auxiliary variables of the same differential order as the stresses. The equilibrium equations, the Beltrami-Michell equations of compatibility and the definitions of the auxiliary variables are used to write a first order matrix differential equation. The solution of this non-self adjoint equation yields a series of non-orthogonal vector eigenfunctions. The coefficients of this series are chosen by use of a generalized biorthogonality condition. Numerical solutions of trial problems are presented as an indication of the rate of convergence of this series.