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The main purpose of this paper is to consider the differential equation u = P (z)u (m ≥ 2) where P is a polynomial with complex, in general, coefficients. Let zk(u), k = 1, 2, . . . be the zeros of a nonzero solution u to that equation. We obtain bounds for the sums j

electronic journal on the qualitative theory of differential equations

Bounds for the sums of zeros of solutions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mrow><mml:mo form="prefix">(</mml:mo><mml:mi>m</mml:mi><mml:mo form="postfix">)</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mrow><mml:mo form="prefix">(</mml:mo><mml:mi>z</mml:mi><mml:mo form="postfix">)</mml:mo></mml:mrow><mml:mi>u</mml:mi></mml:mrow></mml:math>where<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><…

Bounds for the sums of zeros of solutions ofu(m)=P(z)uwhere<…