The authors address the complex oscillation problems of all solutions homogenous linear differential equations with meromorphic coefficients. Sufficient conditions for estimating growth solution infinite order have been proposed based on Nevanlinna value distribution theory. Compared existing results, hyper-order can be estimated in terms a bounded interval which includes information functions ...

We obtain a new version of Hardy theorem about power series several variables reciprocal to the with positive coefficients. prove that if sequence {as} = as1,s2,...,sn, ||s|| ≥ K satisfies condition logarithmically convexity and first coefficient a0 is sufficiently large then has only negative coefficients {bs} bs1,s2,...,sn, except b0,0,...,0 for any K. The classical corresponds case 0, n 1. S...

The canonical solutions of the truncated Hamburger moment problem (both in the classical and degenerate cases) are found. The Nevanlinna theorem which provides the noncanonical solutions of the truncated Hamburger problem is also rederived in the framework of the operator approach.

A genericity condition is removed from a result of Agler and Young which reduces the spectral Nevanlinna-Pick problem in two dimensions to a family of classical Nevanlinna-Pick problems. Unlike the original approach, the argument presented here does not involve state-space methods.

We give an elementary proof of Sarason’s solvability criterion for the Nevanlinna-Pick problem with boundary interpolation nodes and boundary target values. We also give a concrete parametrization of all solutions of such a problem. The proofs are based on a reduction method due to Nevanlinna and the fact that reduction of functions corresponds to Schur complementation of the corresponding Pick...

A linear parabolic differential equation on a moving surface is discretized in space by evolving surface finite elements and in time by backward difference formulas (BDF). Using results from Dahlquist’s G-stability theory and Nevanlinna & Odeh’s multiplier technique together with properties of the spatial semi-discretization, stability of the full discretization is proven for the BDF methods up...

We investigate the singular Weyl–Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x) ∈ L(0, 1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular m-function bel...

We determine all cases when there exists a meromorphic solution of the ODE νw + bw + μw + w/2 +A = 0. This equation describes traveling waves solutions of the KuramotoSivashinsky equation. It turns out that there are no other meromorphic solutions besides those explicit solutions found by Kuramoto and Kudryashov. The general method used in this paper, based on Nevanlinna theory, is applicable t...

Sharp versions of some classical results in differential equations are given. Main results consists of a Clunie and a Mohon’ko type theorems, both with sharp forms of error terms. The sharpness of these results is discussed and some applications to nonlinear differential equations are given in the conluding remarks. Moreover, a short introduction on the connection between Nevanlinna theory and ...

is positive semidefinite for every choice of an integer n and of n points z1, . . . , zn ∈ D. The significance of this characterization for interpolation theory is that it gives the necessity part in the Nevanlinna-Pick interpolation theorem: given points z1, . . . , zn ∈ D and w1, . . . , wn ∈ C, there exists w ∈ S with w(zj) = wj for j = 1, . . . , n if and only if the associated Pick matrix ...