Existence of solutions with turning points for nonlinear singularly perturbed boundary-value problems

We consider the following singularly perturbed boundary-value problem:

Oscillation of neutral delay difference equations of second order with positive and negative coefficients

This paper is concerned with a class of neutral difference equations of second order with positive and negative coefficients of the forms

Composition operators on the Lipschitz space in polydiscs

Let Un be the unit polydisc of Cn and φ= (φ1,...,φn? a holomorphic self-map of Un. Let 0≤α< 1. This paper shows that the composition operator Cφ, is bounded on the Lipschitz space Lipa(Un) if and only if there exists M > 0 such thatfor z∈Un. Moreover Cφ is compact on Lipa(Un) if and only if Cφ is bounded on Lipa(Un) and for every ε > 0, there exists a δ > 0 such that whenever dist(φ(z),σUn) <δ     

Convex mappings on some Reinhardt domains

In this paper, we consider the following Reinhardt domains. Let M = （M1, M2,..., Mn） ： [0,1] → [0,1]^n be a C2-function and Mj（0） = 0, Mj（1） = 1, Mj″ 〉 0, C1jr^pj-1 〈 Mj′（r） 〈 C2jr^pj-1, r∈ （0, 1）, pj 〉 2, 1 ≤ j ≤ n, 0 〈 C1j 〈 C2j be constants. Define
DM={z=（z1,z2,…,Zn）^T∈C^n：n∑j=1 Mj（｜zj｜）〈1}
Then DM C^n is a convex Reinhardt domain. We give an extension theorem for a normalized biholomorphic convex mapping f ： DM -→ C^n.     

非Lipschitz条件下严格伪压缩映射不动点的逼近

Abstract. Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces,the Ishikawa iteration     

Viscosity approximation methods for monotone mappings and a countable family of nonexpansive mappings

We use viscosity approximation methods to obtain strong convergence to common fixed points of monotone mappings and a countable family of nonexpansive mappings. Let C be a nonempty closed convex subset of a Hilbert space H and P _C is a metric projection. We consider the iteration process {x _n } of C defined by x ₁ = x ∈ C is arbitrary and

Zero Distribution of Composite Polynomials and Polynomials Biorthogonal to Exponentials

We analyze polynomials P _n that are biorthogonal to exponentials , in the sense that

Automorphic L-Functions in the Weight Aspect

Let S_k(Γ) be the space of holomorphic Γ-cusp forms f(z) of even weight k ≥ 12 for Γ = SL(2, ℤ), and let S_k(Γ)⁺ be the set of all Hecke eigenforms from this space with the first Fourier coefficient a_f(1) = 1. For f ∈ S_k(Γ)⁺, consider the Hecke L-function L(s, f). Let

Atomic Decomposition of Hardy Spaces Associated with Certain Laguerre Expansions

Let L _n ^a (x), n=0,1,…, be the Laguerre polynomials of order a>−1. Denote ℓ _n ^a (x)=(n!/Γ(n+a+1))^1/2 L _n ^a (x)e ^−x/2. Let

Approximating common fixed points of asymptotically nonexpansive mappings by composite algorithm in Banach spaces

Let E be a uniformly convex Banach space and K a nonempty convex closed subset which is also a nonexpansive retract of E. Let T ₁, T ₂ and T ₃: K → E be asymptotically nonexpansive mappings with {k _n }, {l _n } and {j _n }. [1, ∞) such that Σ _n=1 ^∞ (k _n − 1) < ∞, Σ _n=1 ^∞ (l _n − 1) < ∞ and Σ _n=1 ^∞ (j _n − 1) < ∞, respectively and F nonempty, where F = {x ∈ K: T _1x = T _2x = T ₃ x} = x} denotes the common fixed points set of T ₁, _{T 2} and T ₃. Let {α _n }, {α′ _n } and {α″ _n } be real sequences in (0, 1) and ∈ ≤ {α _n }, {α′ _n }, {α″ _n } ≤ 1 − ∈ for all n ∈ N and some ∈ > 0. Starting from arbitrary x ₁ ∈ K define the sequence {x _n } by

On the limit laws of the second order for additive functionals of Harris recurrent Markov chains

Let {X _n } _{n ≥0} be a Harris recurrent Markov chain with state space E and invariant measure π. The law of the iterated logarithm and the law of weak convergence are given for the additive functionals of the form

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

Expansion of derivatives in one-dimensional dynamics

We study the expansion of derivatives along orbits of real and complex one-dimensional mapsf, whose Julia setJ _f attracts a finite setCrit of non-flat critical points. Assuming that for eachcεCrit, either |D f ⁿ(f(c))|→∞ (iff is real) orb _n·|Df ⁿ(f(c))|→∞ for some summable sequence {b _n} (iff is complex; this is equivalent to summability of |D f ⁿ(f(c))|⁻¹), we show that for everyxεJ _f\U _i f ⁻ⁱ(Crit), there existℓ(x)≤max _c ℓ(c) andK′(x)>0

On the Diophantine Equation G n ( x )?= G m ( P ( x ))

 Let K be a field of characteristic 0 and let p, q, G ₀ , G ₁ , P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G _n (x)) _n=0 ^∞ be defined by the second order linear recurring sequence

Almost sure convergence of sample range

Let X ₁, X ₂, ... be i.i.d. random variables. The sample range is R _n = max {X _i , 1 ≤ i ≤ n} − min {X _i , 1 ≤ i ≤ n}. If for a non-degenerate distribution G and some sequences (α _k ), (β _k ) then we have

On the action of Lipschitz functions on vector-valued random sums

Let X be a Banach space and let (ξ_j)_j ≧ 1 be an i.i.d. sequence of symmetric random variables with finite moments of all orders. We prove that the following assertions are equivalent:

Asymptotic properties of solutions of semilinear second-order elliptic equations in cylindrical domains

The equations under consideration have the following structure:

Approximation of several dimensional functions by trigonometric polynomials

Let f(x, y) be a periodic function defined on the region D

Solutions to Some Open Problems in Fluid Dynamics

Let u=u（x,t,uo）represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt＋δux＋γHuxx＋βuxxx＋f（u）x=αuxx,u（x,0）=uo（x）, whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f（0）=0,｜f（u）｜→∞as ｜u｜→∞,and f∈C^1（R）,and there exist the following limits Lo=lim sup/u→o f（u）/u^3 and L∞=lim sup/u→∞ f（u）/u^5 Suppose that the initial function u0∈L^I（R）∩H^2（R）.By using energy estimates,Fourier transform,Plancherel＇s identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv（xxt）＋δvx＋γHv（xx）＋βv（xxx）=αv（xx）,v（x,0）=vo（x）, the author justifies the following limits（with sharp rates of decay） lim t→∞[（1＋t）^（m＋1/2）∫｜uxm（x,t）｜^2dx]=1/2π（π/2α）^（1/2）m!!/（4α）^m[∫R uo（x）dx]^2, if∫R uo（x）dx≠0, where 0!!=1,1!!=1 and m!!=1·3…（2m-3）…（2m-1）.Moreover lim t→∞[（1＋t）^（m＋3/2）∫R｜uxm（x,t）｜^2dx]=1/2π（x/2α）^（1/2）（m＋1）!!/（4α）^（m＋1）[∫Rρo（x）dx]^2, if the initial function uo（x）=ρo′（x）,for some functionρo∈C^1（R）∩L^1（R）and∫Rρo（x）dx≠0.     

Generating functions and companion symmetric linear functionals

In this contribution we analyze the generating functions for polynomials orthogonal with respect to a symmetric linear functional u, i.e., a linear application in the linear space of polynomials with complex coefficients such that . In some cases we can deduce explicitly the expression for the generating function