Ordinary Differential Equations

  title={Ordinary Differential Equations},
  author={John Charles Burkill and Garrett Birkhoff and Gian-Carlo Rota},
  journal={The Mathematical Gazette},

Linear Ordinary Differential Equations

This is the first of two chapters concerning linear systems and equations. We have already established the unique existence of solutions to initial value problems concerning them. However, because of


Abstract In this note we study the zeros of solutions of differential equations of the form u′′+pu=0. A criterion for oscillation is found, and some sharper forms of the Sturm comparison theorem are

Asymptotic almost periodicity of solutions of a system of differential equations

1. K. M. Das, Singularity-free regions for solutions of 2nd order non-linear dzfferential equations, J. Math. Mech. 13 (1964), 73-84. 2. P. Hartman, Ordinary differential equations, Wiley, New York,

Asymptotic analysis of some nonlinear problems using Hopf-Cole transform and spectral theory

We consider initial boundary value problems for certain nonlinear scalar parabolic equations. A formula for the unique classical solution by Hopf-Cole transformations is obtained and the asymptotic

Global solutions to a class of nonlinear damped wave operator equations

This study investigates the existence of global solutions to a class of nonlinear damped wave operator equations. Dividing the differential operator into two parts, variational and non-variational

Periodic solution of a second order, autonomous, nonlinear system

There exist a sufficient condition for the existence of at least one periodic solution for a type of second order autonomous ordinary differential equations. The correctness of the condition has been

Closed form numerical solutions of variable coefficient linear second-order elliptic problems