Abstract
Let p be a real continuous function of the real variable x on [a,b]. If the differential equation
has a nontrivial solution y that vanishes at two points of [a,b], then, according to A. M. Lyapunov [1], p is subject to the inequality
This inequality is sharp in the sense that the constant 4 cannot be replaced by a larger number.
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Mitrinović, D.S., Pečarić, J.E., Fink, A.M. (1991). Inequalities of Lyapunov and of De La Vallée Poussin. In: Inequalities Involving Functions and Their Integrals and Derivatives. Mathematics and Its Applications, vol 53. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3562-7_6
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