On the existence of T-direction of algebroid functions: A problem of J.H. Zheng

In this paper, we solve a problem of J.H. Zheng (see Problem 5.12 of [J.H. Zheng, On value distribution of meromorphic functions with respect to arguments, preprint]) by proving that for any ν-valued algebroid function satisfying , there exists a T-direction dealing with multiple values of w(z).     

Difference equations of second order with spectral singularities

In this paper using the uniqueness theorem of analytic functions we investigated the eigenvalues and the spectral singularities of the difference equation

     

On the meromorphic solutions of linear differential equations on the complex plane

In this paper we investigate the iterated order, iterated type and iterated convergence exponent of zeros of meromorphic solutions of the equations

     

Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source

In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations

in Ω×(0,T) with initial and Dirichlet boundary conditions, where Ω is a bounded domain in . Under suitable assumptions on the functions g_i(), , the initial data and the parameters in the equations, we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property.     

The existence and uniqueness of energy solutions to local non-Lipschitz stochastic evolution equations

Let H,V and K be separable Hilbert spaces. In this paper we consider the existence and uniqueness of energy solutions to the following stochastic evolution equation:

where is a linear bounded operator with coercivity, monotone condition and hemicontinuity, and are measurable functions and satisfy the local non-Lipschitz condition proposed by the author [T. Taniguchi, Successive approximations to solutions of stochastic differential equations, J. Differential Equations 96 (1992) 152–169].     

Explicit description for the automorphism group of the Fornæss domain

Motivated by the Kohn-Nirenberg domain, J.E. Fornæss considered the germ of a domain near the origin in C² such that

     

On uniqueness criteria for systems of ordinary differential equations

We present some new uniqueness criteria for the Cauchy problem

     

Existence and uniqueness of solutions of semilinear stochastic infinite-dimensional differential systems with H-regular noise

Existence and uniqueness of approximate strong solutions of stochastic infinite-dimensional systems

     

Uniqueness of positive solutions for semilinear elliptic systems

We prove uniqueness of positive solutions for the system

     

On the uniqueness of discontinuous solutions to the Degasperis-Procesi equation

We prove uniqueness within a class of discontinuous solutions to the nonlinear and third order dispersive Degasperis-Procesi equation

     

Boundary blow-up solutions for a cooperative system of quasilinear equation

We study the existence, uniqueness and boundary behavior of positive boundary blow-up solutions to the quasilinear elliptic system

     

Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives

We discuss existence, uniqueness and stability of solutions of the system of nonlinear fractional differential equations

     

A sharp form of an embedding into exponential and double exponential spaces

Let Ω be a bounded domain in . In the well-known paper (Indiana Univ. Math. J. 20 (1971) 1077) Moser found the smallest value of K such that

     

Stochastic evolution equations in UMD Banach spaces

We discuss existence, uniqueness, and space-time Hölder regularity for solutions of the parabolic stochastic evolution equation

     

Classical solutions of singular Monge-Ampère equations in a ball

Our concern is on existence, uniqueness and regularity of convex, negative, radially symmetric classical solutions to

     

Solvability for second-order three-point boundary value problems at resonance on a half-line

This paper deals with the solvability and uniqueness of the second-order three-point boundary value problems at resonance on a half-line

     

Regularity for a fourth-order critical equation with gradient nonlinearity

Given Ω a smooth bounded domain of Rn, n?3, we consider functions that are weak solutions to the equation

     

Hardy-type theorem for orthogonal functions with respect to their zeros. The Jacobi weight case

Motivated by the G.H. Hardy's 1939 results [G.H. Hardy, Notes on special systems of orthogonal functions II: On functions orthogonal with respect to their own zeros, J. London Math. Soc. 14 (1939) 37-44] on functions orthogonal with respect to their real zeros λn, , we will consider, under the same general conditions imposed by Hardy, functions satisfying an orthogonality with respect to their zeros with Jacobi weights on the interval (0,1), that is, the functions f(z)=zνF(z), ν∈R, where F is entire and

     

Existence and uniqueness of multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields

In this paper, we are concerned with the existence and uniqueness of multi-bump bound states of the nonlinear Schrödinger equations with electromagnetic potential

     

Stochastic functional Kolmogorov-type population dynamics

In this paper we stochastically perturb the functional Kolmogorov-type system

into the stochastic functional differential equation

This paper studies existence and uniqueness of the global positive solution, and its asymptotic bound properties and moment average in time. These properties are natural requirements from the biological point of view. As the special cases, we discuss the various stochastic Lotka–Volterra systems.