Continuity Conditions for a Class of Gaussian Chaos Processes Related to Continuous Additive Functionals of Lévy Processes

Let be sequences of real numbers which are symmetric in k. Let be independent sequences of independent normal random variables with mean zero and variance one. For each fixed choice of we consider

Sums of Five, Seven and Nine Squares

Let r _k(n) denote the number of representations of an integer n as a sum of k squares. We prove that

Existence and Uniqueness of a Weak Solution to the Initial Mixed Boundary-Value Problem for Quasilinear Elliptic-Parabolic Equations

We prove the existence and the uniqueness of a weak solution to the mixed boundary problem for the elliptic-parabolic equation

On functional equations associated with characters of unitary representations of groups

This is mainly concerned with the following functional equation:

Bifurcation problems for superlinear elliptic indefinite equations with exponential growth

This paper deals with the existence and the behaviour of global connected branches of positive solutions of the problem

Estimate of fourier transforms with respect to the system of generalized eigenfunctions of the Schrödinger operator with Stummel-type potential

Suppose thatА is a nonnegative self-adjoint extension to { } of the formal differential operator−Δu+q(x)u with potentialq(x) satisfying the condition {

Sharp Pointwise Interpolation Inequalities for Derivatives

We prove new pointwise inequalities involving the gradient of a function , the modulus of continuity of the gradient , and a certain maximal function and show that these inequalities are sharp. A simple particular case corresponding to and is the Landau type inequality , where the constant 8/3 is best possible and

L ∞-solutions for some nonlinear degenerate elliptic and parabolic equations

In this paper we prove the existence of bounded solutions for equations whose prototype is:

Commutativity of rings through a Streb's result

In this paper we investigate commutativity of rings with unity satisfying any one of the properties:

Oscillation of nonlinear differential systems with retarded arguments

In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form

Oscillation Theorems for Quasilinear Elliptic Differential Equations

By using vector Riccati transformation and averaging technique, some oscillation criteria for the quasilinear elliptic differential equation of second order, ΣNi,j=1Di[Ψ（y）Aij（x）｜Dy｜^p-2Djy]＋p（x）f（y）=0, are obtained. These theorems extend and include earlier results for the semilinear elliptic equation and PDE with p-Laplacian.     

多线性分数次积分算子交换子的有界性

Ibαf ( x) =∫R ∏mj=1( bj( x) - bj( y) ) 1| x - y| n-αf ( y) dyare considered.The following priori estimates are proved.For 1 01Φ1t| {y∈Rn:| Ibαf( y) | >t}| 1q ≤csupt>01Φ1t| {y∈Rn:ML( log L) 1r ,α(‖b‖f ) ( y) >t}| 1q,where‖b‖=∏mj=1‖bj‖Oscexp Lrj,Φ( t) =t( 1 + log+t) 1r,1r =1r1+ ...+ 1rm,ML(…     

Oscillatory properties of solutions of three-dimensional differential systems of neutral type

The purpose of this paper is to obtain oscillation criteria for the differential system

Uniform estimates of positive solutions to quasi-linear differential equations

One considers the differential inequality

An isolic generalization of Cauchy's theorem for finite groups

In his note [5] Hausner states a simple combinatorial principle, namely:

An Elementary Proof of Pólya-Vinogradov's Inequality, II

Let be a primitive character mod k, k > 2. In [1], the following elementary estimate

Oscillation of certain difference equations

Some new criteria for the oscillation of difference equations of the form

A Problem with Nonlocal Boundary Conditions for a Quasilinear Parabolic Equation

The solvability of the nonlocal boundary value problem

A Generalized Measure Concentrated on a Closed Set of Measure Zero

When E is a closed set of measure zero in the dyadic group and the Walsh series satisfies

Unbounded solutions of a nonlinear parabolic equation

The article investigates the equation