multiple interpolation with the fast-growing knots in the class of entire functions and its application

the conditions for the sequence of complex numbers (bn,k) are obtained, such that the interpolation problem g(^𝑘-1)(λn) = bn,𝑘, 𝑘 ∈ 1, s, n ∈ n, where |λ𝑘/λ𝑘+1| ≤ ∆ 1, has a unique solution in some classes of entire functions g for which mg(r) ≤ c1 exp ((s 1)n(r) + n(ρ1r)), where n(r) is the counting function of the sequence (λn), ρ1 ∈ (∆; 1), and c1 0. moreover, these results have been applied to the description of the solution of the differential equation f^(s) +𝐴𝑂(𝑧)f = 0 for which (λn) is zerosequence and the coeffcient 𝐴𝑂 is an entire function from the mentioned class.