FINITE TRAVELING WAVES FOR A REACTION-DIFFUSION SYSTEM WITH N（≥3） COMPONENTS

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Approximating periodic functions by interpolation sums of Jackson type

Let

Chaos and asymptotical stability in discrete-time recurrent neural networks with generalized input-output function

We theoretically investigate the asymptotical stability, local bifurcations and chaos of discrete-time recurrent neural networks with the form of

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

Oscillation Theorems for Nonlinear Second Order Elliptic Equations

Some oscillation theorems are given for the nonlinear second order elliptic equationsum from i,j=1 to N D_i[a_(ij)(x)Ψ(y)||▽y||~(p-2)D_(jy)] c(x)f(y)=0.The results are extensions of modified Riccati techniques and include recent results of Usami.     

Behavior of Solutions of Quasilinear Elliptic Inequalities

The paper considers solutions of the coercive inequalities

Averaging and fluctuations for parabolic equations with rapidly oscillating random coefficients

In this paper we consider the parabolic equation with random coefficients:

Boundedness of Marcinkiewicz integral related to multilinear commutators with variable kernels on Hardy spaces

Let→b=(b1,b2,…,bm),bi∈∧βi(Rn),1≤I≤m,βi＞0,m∑I=1βi=β,0＜β＜1,μΩ→b(f)(x)=(∫∞0|F→b,t(f)(x)|2dt/t3)1/2,F→b,t(f)(x)=∫|x-y|≤t Ω(x,x-y)/|x-y|n-1 mΠi=1[bi(x)-bi(y)dy.We consider the boundedness of μΩ,→b on Hardy type space Hp→b(Rn).     

Continuous dependence on the boundary conditions for the Wentzell Laplacian

The solution u of the well-posed problem

On Sidon-Telyakovskii-type conditions for the integrability of multiple trigonometric series

For a trigonometric series

Generalized sine equations,II

In this paper we solve the equations

Approximating periodic functions in Hölder type metrics by singular integrals with positive Kernels

Let M be either the space of 2π-periodic functions L_p, where 1 ≤ p < ∞, or C; let ω_r(f, h) be the continuity modulus of order r of the function f, and let

Construction of a solution of a mixed problem for the generalized heat conduction equation by the fourier method

By the Fourier method a solution of the equation

Partial regularity for minimisers of certain functionals having nonquadratic growth

We prove partial regularity results for local minimisers of

Averaging technique for the oscillation of second order damped elliptic equations

By using the averaging technique, we establish some oscillation theorems for the second order damped elliptic differential equation N↑∑↓i,j=1 Di[AIY（x）Djy]＋N↑∑↓i=1 bi（x）Diy＋c（x）f（y）=0 which extend and improve some known results in the literature.     

The Law of the Iterated Logarithm for Functionals of Harris Recurrent Markov Chains: Self Normalization

Let {X _n } _n0 be a Harris recurrent Markov chain with state space E, transition probability P(x, A) and invariant measure , and let f be a real measurable function on E. We prove that with probability one,

Identities Involving Coefficients of Automorphic L-Functions

Let f(z) be a holomorphic Hecke eigenform of weight k with respect to SL(2, ℤ) and let

Notes on infinite-dimensional nonlinear parabolic equations

We present a method for the solution of the Cauchy problem for three broad classes of nonlinear parabolic equations

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.