On a problem in complex oscillation theory of periodic second order linear differential equations and some related perturbation results.
On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem
2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.In this paper we study an ODE in the complex plane. This is a key step in the search of new necessary conditions for the well posedness of the Cauchy Problem for hyperbolic operators with double characteristics.
On analytic and meromorphic functions satisfying nth order algebraic differential equations in regions of the plane.
On commuting differential operators.
On commuting matrix differential operators.
On meromorphic solutions of a certain class of functional-differential equations
On Meromorphic Solutions of First-Order Differential Equations
On meromorphic solutions of the Riccati differential equations
We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation w' = a(z) + b(z)w + w², where a(z) and b(z) are meromorphic functions. In particular, we correct a result of E. Hille [Ordinary Differential Equations in the Complex Domain, 1976] and get a precise estimate on the growth order of the transcendental meromorphic solution w(z); and if at least one of a(z) and b(z) is non-constant, then we show that w(z)...
On subnormal solutions of periodic differential equations.
On the existence of meromorphic solutions of differential equations having arbitarily rapid growth.
On the growth and factorization of entire solutions to algebraic differential equations.
On the growth of an algebroid function with radially distributed values
We investigate how the growth of an algebroid function could be affected by the distribution of the arguments of its a-points in the complex plane. We give estimates of the growth order of an algebroid function with radially distributed values, which are counterparts of results for meromorphic functions with radially distributed values.
On the growth of meromorphic solutions of linear and algebraic differential equations.
On the hyper order of solutions of a class of higher order linear differential equations.
On the Location of Zeros of Solutions of f'' + A(z)f = 0 where A(z) is Entire.
On the meromorphic solutions of a certain type of nonlinear difference-differential equation
The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation where is a difference-differential polynomial in of degree with small functions of as its coefficients, , are nonzero rational functions and , are non-constant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation.
On the zeros and hyper-order of meromorphic solutions of linear differential equations.
On the zeros of meromorphic solutions of second-order linear differential equations.
Order of growth of solutions to algebraic differential equations in the unit disk.
Oscillation results on meromorphic solutions of second order differential equations in the complex plane.