相关论文: Bank-Laine functions, the Liouville transformation…

It is known that a Bank-Laine function $E$ is a product of two normalized solutions of the second order differential equation $f"+Af=0$ $(\dagger)$, where $A=A(z)$ is an entire function. By using Bergweiler and Eremenko's method of…

Every real Bank-Laine function of finite order, whose zeros are all real but neither bounded above nor bounded below, either has an explicit representation in terms of trigonometric functions or has zeros with exponent of convergence at…

A Bank--Laine function $E$ is written as $E=f_1f_2$ for two normalized solutions $f_1$ and $f_2$ of the second order differential equation $f''+Af=0$, where $A$ is an entire function. In this paper, we first complete the construction of…

Some results are proved concerning asymptotic and deficient values in connection with the second order linear differential equation $y'' + Ay = 0$, in which the coefficient $A$ is entire.

We resolve a question of Bank and Laine on the zeros of solutions of $w'' + Aw = 0$ where $A$ is an entire function of finite order.

We describe a new method of constructing transcendental entire functions $A$ such that the differential equation $w"+Aw=0$ has two linearly independent solutions with relatively few zeros. In particular, we solve a problem of Bank and Laine…

Eremenko and Lyubich proved that an entire function whose set of singular values is bounded is expanding at points where its image has large modulus. These expansion properties have been at the centre of the subsequent study of this class…

New necessary and sufficient conditions are given for the quantization of a class of periodic second order non-homogeneous ordinary differential equations in the complex plane in this paper. The problem is studied from the viewpoint of…

We introduce a new technique that allows us to make progress on two long standing conjectures in transcendental dynamics: Baker's conjecture that a transcendental entire function of order less than 1/2 has no unbounded Fatou components, and…

We apply Kovacic's algorithm from differential Galois theory to show that all complex non-oscillatory solutions (finite exponential of convergence of zeros) of certain Hill equations considered by Bank and Laine using Nevanlinna theory must…

The Eremenko-Lyubich class of transcendental entire functions with a bounded set of singular values has been much studied. We give a new characterisation of this class of functions. We also give a new result regarding direct singularities…

Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…

It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…

This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…

Using the same heuristic argument leading to the Lang-Waldschmidt Conjecture in the theory of linear forms in logarithms, we formulate an effective version of the Linear Independence conjecture for the ordinates of the non-trivial zeros of…

For a second order linear differential equation $f''+A(z)f'+B(z)f=0$, with $ A(z)$ and $B(z)$ being transcendental entire functions under some restriction, we have established that all non-trivial solutions are of infinite order. In…

The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…

Brjuno and R\"ussmann proved that every irrationally indifferent fixed point of an analytic function with a Brjuno rotation number is linearizable, and Yoccoz proved that this is sharp for quadratic polynomials. Douady conjectured that this…

We prove a Liouville type classification theorem in half-spaces for infinite boundary value problems related to fully nonlinear, uniformly elliptic operators. We then apply the result in order to obtain gradient boundary blow up rates for…

We show that if a 1-hyperbolic structurally finite entire function of type $(p,q)$, $p\ge 1$, is linearizable at an irrationally indifferent fixed point, then its multiplier satisfies the Brjuno condition. We also prove the generalized…