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 y + λ ^2 p(t)y = 0, y(0) = 0, y(0) = 1 with p(t) satisfying one of the following conditions: (i) |p(t)| M< ∞ ; (ii) 0< ω _1 p(t) ω _2< ∞ ; (iii) sup_x _x^x + T p(t)dt = P_T /T. The extremal solutions are found.