An Elementary Proof Of An Oscillation Theorem For Differenti

An Elementary Proof of an Oscillation Theorem for Differential Equations

Author: Robert Gethner

College Mathematics Journal, Vol. 38, No. 4 (Sep, 2007), pp. 301–303

This paper explores what can be learned about the solutions of y''+q(t)y=0 using arguments from elementary calculus. This equation is seen in many applications, including spring-mass problems and vibrating membrane. This latter application leads to Bessel’s equation. The author states the Sturm Comparison Theorem, which gives information on the zeros of any solution to y''+q(t)y=0. Using calculus, he then proves that the number of zeros of a solution will be unbounded if q(t) is bounded below by a positive constant for t>0. These results are important because they confirm that the predictions of a model agree with our physical intuition.

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