Glasnik Matematicki, Vol. 50, No. 1 (2015), 183-192.

SUMS OF ZEROS OF SOLUTIONS TO SECOND ORDER DIFFERENTIAL EQUATIONS WITH POLYNOMIAL COEFFICIENTS

Michael Gil'

Department of Mathematics , Ben Gurion University of the Negev, P.0. Box 653, Beer-Sheva 84105, Israel
e-mail: gilmi@bezeqint.net


Abstract.   We consider the equation u''=P(z)u, where P(z) is a polynomial. Let zk(u), k=1, 2, ... be the zeros of a solution u(z) to that equation. Inequalities for the sums k=1j |zk(u)|-1 (j=1, 2, ...) are derived. They considerably improve the previous result of the author. Some applications of the obtained bounds are also discussed. An illustrative example is presented. It shows that the suggested results are sharp.

2010 Mathematics Subject Classification.   34C10, 34A30.

Key words and phrases.   Linear differential equation in the complex plane, bounds for zeros of solutions.


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DOI: 10.3336/gm.50.1.10


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