I am looking for a (simple) first order differential equations model
(that models anything physical eg mixture problem or similar to
predator-prey model) that HAS NON-UNIQUE solutions. That is, the
uniqueness theorem fails. This happens when the differential equation
is not continuous and its derivitive is not continuous either.

It should be a model. A clear explanation of the model is greatly
appreciated with the equations solved, the variables explained and the
non-uniqueness failiure checked. The model can be simple, i dont need
an advanced model, but the diffrential equation should model something
but should not be continuous.

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Clarification of Question by asadmu-ga on 01 Feb 2005 21:56 PST

e.g i would like:  to illustrate the application of the Theorem of
existence and uniqueness. So if you could provide one example of a
real world problem which can be used to explain that if the condition
to the Theorem is not satisfied, the solution will not be unique.

    * (a). State the real world problem,
    * (b). Define variables and write a differential equation to model
the problem(process),
    * (c). Solve the model equation,
    * (d). Discuss and explain the results.

I believe the predator-prey problem can be so modeled and is
discontinuous at the initial and terminal points. Check out
"Generalized solutions of the pursuit problem in three-dimensional
Euclidean space" by O. Ibidapo-Obea, O. S. Asaolu and A. B. Badiru in
Applied Mathematics and Computation
Volume 119, Issue 1 , 25 March 2001, Pages 35-45