2019
Том 71
№ 11

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Estimation of the solutions of the Sturm-Liouville equation

Levin B. Ya., Mirochnik L. Ya.

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Abstract

Exact estimates are presented for the solutions of the problem $\ddot y + \lambda ^2 p(t)y = 0, y(0) = 0, \dot y(0) = 1$ with $p(t)$ satisfying one of the following conditions: $$(i) |p(t)| \leqslant M< \infty ; (ii) 0< \omega _1 \leqslant p(t) \leqslant \omega _2< \infty ; (iii) \mathop {sup}\limits_x \int_x^{x + T} {p(t)dt = P_T /T.}$$ The extremal solutions are found.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 3, pp 251-289.

Citation Example: Levin B. Ya., Mirochnik L. Ya. Estimation of the solutions of the Sturm-Liouville equation // Ukr. Mat. Zh. - 1994. - 46, № 3. - pp. 244–278.

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