AbstractAn efficient condition is established ensuring that on any interval of length ω,
any nontrivial solution of the equation ${u^{\prime\prime}=p(t)u}$ has at most one zero.
Based on this result, the unique solvability of a periodic boundary value problem is studied.
Abstract
It is shown that the differential equation
u
(n) = p(t)u,
where n ≥ 2 and p : [a, b] → ℝ is a summable function, is not conjugate in the segment [a, b], if for some l ∈ {1, . . . , n – 1}, α ∈]a, b[ and β ∈]α, b[ the inequalities
hold.
Some properties of the solutions of third order linear ordinary differential equations
