一阶时滞微分方程解的零点分布

Abstract. The paper gives two estimates of the distance between adjacent zeros of solutions     

Oscillation and Nonoscillation Criteria for a Second Order Linear Equation

New oscillation and nonoscillation criteria are established for the equation

On the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Singular Hyperbolic Equations

In the rectangle D = (0,

Some rapidly converging series for

For a natural number , the author derives several families of series representations for the Riemann Zeta function . Each of these series representing converges remarkably rapidly with its general term having the order estimate:

Relevant connections of the results presented here with many other known series representations for are also pointed out.

     

approximations of inertial manifolds via finite differences

We construct an inertial manifold for the evolution equation as a limit of the inertial manifolds for the difference approximations of the Trotter-Kato type and show that this limit is taken in a topology.

     

On the Prandtl Equation

The unique solvability of the airfoil (Prandtl) integro-differential equation on the semi-axis ⁺ = [0, ) is proved in the Sobolev space W _p ¹ and Bessel potential spaces H _p ^s under certain restrictions on p and s.     

Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case

We establish global wellposedness and scattering for the -critical defocusing NLS in 3D

assuming radial data , . In particular, it proves global existence of classical solutions in the radial case. The same result is obtained in 4D for the equation

     

Weighted Caccioppoli-type estimates and weak reverse Hölder inequalities for -harmonic tensors

We obtain a local weighted Caccioppoli-type estimate and prove the weighted version of the weak reverse Hölder inequality for -harmonic tensors.

     

Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients

The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hörmander"s type for the spectral function of pseudodifferential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.     

Abundant Multisoliton Structure of (3+1)-Dimensional Breaking Soliton Equation

Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed.