John S. Spraker

A generalization of the Lane–Emden equation

Abstract We consider a class of second-order initial-value problems, which includes the well-known Lane–Emden equation from astrophysics as a special case. Local existence, global existence and uniqueness of solutions are proven.

Numerical approximation for singular second order differential equations

We consider numerical approximation of solutions of singular second order differential equations. In particular, we study the backward (or implicit) Euler method. We prove results concerning consistency, global error and stability. We show that the global error is linear with respect to the step size. Numerical results are also given, which demonstrate the linear convergence and we compare the numerical results with known approximations.

Fixed point approaches to the solution of integral inclusions

Solutions to generalizations of the Volterra and Hammerstein integral inclusions are found by using the fixed point theorems of Covitz-Nadler and Bohnenblust-Karlin. Several illustrative examples are presented. Some conditions are given which also allow Lipschitz solutions to be obtained.

Results on Uniqueness of Solutions for a Generalized Second Order Differential Equation

ABSTRACT We present two theorems concerning uniqueness of solutions for second order ordinary differential equations that have a generalized left-hand side with initial conditions. Despite the fact that the hypotheses are weak, the theorems cover a large number of cases and the proofs are not especially complicated.