Summary: The conditions for the sequence of complex numbers \((b_{n,k})\) are obtained, such that the interpolation problem \(g^{(k-1)}( \lambda_n) = b_{n,k} \), \(k \in \overline{1,s}\), \( n \in \mathbb N\), where \(| \lambda / \lambda_{k+1}| \leq \Delta < 1\), has a unique solution in some classes of entire functions \(g\) for which \(M_g(r) \leq c_1 \exp ((s-1) N(r) + N(\rho_1r))\), where \(N(r)\) is the counting function of the sequence \((\lambda_n) \), \( \rho \in ( \Delta; 1)\) and \(c_1 > 0\). Moreover, these results have been applied to the description of the solution of the differential equation \(f^{(s)} + A_0(z)f = 0\) for which \((\lambda_n)\) is zero-sequence and the coeffcient \(A_0\) is an entire function from the mentioned class.