Estimation of the solutions of the Sturm-Liouville equation - Levin, B. Ya.; Mirochnik, L. Ya. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
Exact estimates are presented for the solutions of the problem $\ddot y + λ ^2 p(t)y = 0, y(0) = 0, \dot y(0) = 1$ with $p(t)$ satisfying one of the following conditions:$$(i) |p(t)| \leqslant M< ∞ ; (ii) 0< ω _1 \leqslant p(t) \leqslant ω _2< ∞ ; (iii) \mathop {sup}\limits_x \int_x^{x + T} {p(t)dt = P_T /T.}$$The extremal solutions are found.