PROPERTIES OF SOLUTIONS TO A HARMONIC-MAPPING TYPE EQUATION WITH A DIRICHLET BOUNDARY CONDITION

In the present paper, we consider the problem ■ where β₁, β₂ > 0 and β₁ + β₂ < 1, and ? is a convex domain in Rⁿ. The existence, uniqueness,regularity and (2-β₂)/(1-β₁-β₂)-concavity of the positive solutions of the problem(0.1) are proven.     

Complement of the reduced non-zero component graph of free semimodules

Let M be a finitely generated free semimodule over a semiring S with identity having invariant basis number property with a basis α={α₁,...,α_k}.The complement■of the reduced non-zero component graph■ of M,is the simple undirected graph with ■as the vertex set and such that there is an edge between two distinct vertices ■ and ■ if and only if there exists no i such that both a_i,b_i are non-zero.In this paper,we show that the graph■ ...     

Unified Limits and Large Deviation Principles for β-Laguerre Ensembles in Global Regime

Let(λ₁,...,λ_n) be β-Laguerre ensembles with ■parameters β,p,n and■ with for 1≤i≤n.In this paper,as β varies and satisfies lim_n→∞ log n/βn=0,we offer a modified Marchenko-Pastur,law or semicircle law as the weak limits for the sequence μ_n when lim_n→∞ n/p=γ∈(0,1] or lim_n→∞ n/p=0,respectively.This recovers some well-known results.Moreover,we give a full large deviation principle of μ_n with speed βn² and good rat...     

非线性分数次边值问题改进的ADM解法(英文)

We use the modified Adomian decomposition method（ADM） for solving the nonlinear fractional boundary value problem {D（^α₀） + u（x） = f（x, u（x））, 0 < x < 1, 3 < α≤ 4 u（0） = α₀ , u’’ （0） = α₂ u（1） = β₀ , u’’（1） = β₂} （1） where D（₀^α）+u is Caputo fractional derivative and α₀,α₂,β₀,β₂ is not zero at all,and f:[0,1]×R→ R is continuous.The calculated numerical results show reliability and efficiency of the algorithm given.The numerical procedure is tested on linear and nonlinear problems.     

Bounds for Average toward the Resonance Barrier for GL(3) × GL(2) Automorphic Forms

Let f be a fixed Maass form for SL₃(Z) with Fourier coefficients A_f(m,n).Let g be a Maass cusp form for SL₂(G) with Laplace eigenvalue (1/4)+k² and Fourier coefficient λ_g(n),or a holomorphic cusp form of even weight k.Denote by S_X(f×g,α,β) a smoothly weighted sum of A_f(1,n)λ_g(n)e(αn^β)for X 0 are fixed real numbers.The subject matter of the present paper is to prove ...     

LARGE DEVIATIONS FOR TOP EIGENVALUES OF β-JACOBI ENSEMBLES AT SCALING TEMPERATURES

Let λ=(λ₁,…,λ_n) be β-Jacobi ensembles with parameters p₁,p₂,n and β,with β varying with n.Set■.Suppose that■ and 0 ≤σγ <1.We offer the large deviation for p₁+p₂/p₁■ λ_i when γ> 0 via the large deviation of the corresponding empirical measure and via a direct estimate,respectively,when γ=0.     

关于ρ-混合序列的完全收敛性

Let l (x) andβ(x) be even positive fun(?)tions. Suppose there is a censtant θ>0 such that β(x)/x~θ, x~2/β(x) and l(x) (x>0) are monotone nondecreasing Denote α(x) is the converse funotion of β(x). Theerem 1 Suppose there is a constant 0<ε_0<1 such that β(x)l(β(x))/x and x~(2-ε_0)/(β(x)l(β(x))) are monotene nondecreasing. Let {X_k} be a ρ-mixing sequence of identically distributed random varibles with EX_1=0 and Eβ(X_1)l(β(|X_1|))     

Global multiplicity of solutions to a defocusing quasilinear Schr?dinger equation with the singular term

We consider a class of modified quasilinear Schr?dinger equations ■ with u(x)=0 on ??, where ? ? R^N is a bounded domain with a regular boundary, N≥3, a and b are bounded mensurable functions, 0 < α < 1 < β < 2^*-1 and k, λ≥0 are two parameters. We establish the global existence and multiplicity results of positive solutions in H₀¹ (?) ∩ L^∞ (?) for appropriate classes of parameters k and λ and coefficients a(x) and b(x).     

BOUNDEDNESS OF A CHEMOTAXIS-CONVECTION MODEL DESCRIBING TUMOR-INDUCED ANGIOGENESIS

This paper is concerned with the parabolic-parabolic-elliptic system ■in a bounded domain Ω?Rⁿ with a smooth boundary,where the parameters χ,ζ₁,ζ₂ are positive constants and m≥1.Based on the coupled energy estimates,the boundedness of the global classical solution is established in any dimensions(n≥1) provided that m>1.     

THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS

We find the exact forms of meromorphic solutions of the nonlinear differential equations ■,n≥ 3,k≥1,where q,Q are nonzero polynomials,Q■ Const.,and p₁,p₂,α₁,α₂ are nonzero constants with α₁≠α₂.Compared with previous results on the equation p(z)f³+q(z)f"=-sinα(z) with polynomial coefficients,our results show that the coefficient of the term f~((k)) perturbed by multiplying an exponential function will affect the structur...     

Infinitely Many Solutions for a Class of Quasi-linear Elliptic Problem

In this paper,we study the following quasi-linear elliptic equation:■where Ω?R^N is a bounded domain,λ>0 is a parameter.The function ψ(|t|)t is the subcritical term,and φ(|t|)t is the critical Orlicz-Sobolev growth term with respect to φ.Under appropriate conditions on φ,ψ and φ,we prove the existence of infinitely many weak solutions for quasi-linear elliptic equation,for λ∈(0,λ₀),where λ₀> 0 is a fixed constant.     

TWO WEIGHT CHARACTERIZATIONS FOR THE MULTILINEAR LOCAL MAXIMAL OPERATORS

Let 0<β<1 andΩbe a proper open and non-empty subset of Rⁿ.In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_β((f))(x)=sup_Q(∈xQ∈Fβ)Π_i=1^m1/|Q|∫_Q|f_i(y_i)|dy_i,where F_β={Q(x,l):x∈Ω,l<βd(x,Ω^c)},Q=Q(x,l)is denoted as a cube with sides parallel to the axes,and x and l denote its center and half its side length.Two-weight characterizations for the multilinear local maximal operator M_βare obtained.A formulation of the Carleson embedding theorem in the multilinear setting is proved.     

THE EXISTENCE AND NON-EXISTENCE OF SIGN-CHANGING SOLUTIONS TO BI-HARMONIC EQUATIONS WITH A p-LAPLACIAN

We investigate the bi-harmonic problem ■ where Δ² u=Δ（Δu）,Δ_pu=div(|▽u|^p-2▽u) with p> 2.Ω is a bounded smooth domain in R^N,N≥1.By using a special function space with the constraint ∫_Ω udx=0,under suitable assumptions on f and g（x,u）,we show the existence and multiplicity of sign-changing solutions to the above problem via the Mountain pass theorem and the Fountain theorem.Recent results from the literature are extended.     

Scattering for the Radial Schr?dinger Equation with Combined Power-type and Choquard-type Nonlinearities

In this paper,we show the scattering of the radial solution for the nonlinear Schr?dinger equation with combined power-type and Choquard-type nonlinearities■ in the energy space H¹(R^N) for λ₁λ₂=-1.We establish a scattering criterion for radial solution together with Morawetz estimate which implies the scattering theory.Results show that the defocusing perturbation terms does not determine the scattering solution in energy space.     

Monotone Chains in Modulus of Two Classes of Dirichlet Coefficients

Let f₁,...,f_k and g₁,...,q_k be non-CM newforms of square-free levels.Denote byλ_{sym^j fi}(n) the coefficients of the Dirichlet expansion of L(sym^j f_i,s) and ν₁,...,ν_k the distinct positive integers such that λ_{sym^j fi}(ν_i)≠0.In this paper,we obtain that there exist infinitely many positive integers m such that 0 <λ_{sym^j ...}     

The Isomorphism Problem of Normalized Unit Groups of Group Algebras of a Class of Finite 2-groups

Let p be a prime and F_p be a finite field of p elements. Let F_pG denote the group algebra of the finite p-group G over the field F_p and V(F_pG) denote the group of normalized units in F_pG.Suppose that G and H are finite p-groups given by a central extension of the form■ and G’≌Z_p, m ≥ 1. Then V(F_pG)≌V(F_pH) if and only if G≌H. Balogh and Bovdi only solved the isomorphism problem when p is odd. In this paper, th...     

Special John-Nirenberg-Campanato spaces via congruent cubes

Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JN^con_(p,q,s) over Rⁿ or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over Rⁿ or a given cube of Rⁿ with finite side length.Furthermore, some VMO-H¹-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.     

A generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularities

In this paper, using the method of blow-up analysis, we establish a generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularities. Precisely, let(Σ, D) be such a surface∑with divisor D =Σ_(i=1)~mβ_(ipi), where β_i -1 and p_i ∈Σ for i = 1,..., m, and g be a metric representing D.Denote b_0 = 4π(1 + min_(1≤i≤mβ_i). Suppose ψ : Σ→ R is a continuous function with ∫_Σψdv_g ≠0 and define■Then for any α∈ [0, λ_1~(**)(Σ, g)), we have■When b b0, the integrals■are still finite, but the supremum is infinity. Moreover, we prove that the extremal function for the above inequality exists.     

Limit Theorems and Large Deviations for β-Jacobi Ensembles at Scaling Temperatures

Let λ=(λ₁,...,λ_n) be β-Jacobi ensembles with parameters p₁,p₂,n and β while β varying with n. Set γ=lim_n→∞ n/(p1) and σ=lim_n→∞ (p1)/(p2).In this paper,supposing lim_n→∞ log n/βn=0,we prove that the empirical measures of different scaled λ converge weakly to a Wachter distribution,a Marchenko-Pastur law and a semicircle law corresponding to σγ> 0,σ=0 or γ=0,respectively.We also offer a full large deviation principle wi...     

SYNCHRONIZATION OF COMPLEX NETWORKS VIA A SIMPLE AND ECONOMICAL FIXED-TIME CONTROLLER

<正>1 Introduction and Main Results Consider the following differential equation ■where x∈Rⁿ denotes the state variable of system (1.1), f:Rⁿ→Rⁿ is a nonlinear vector field and x₀ is the initial value of the system.Definition 1.1 [1] The origin of system (1.1) is said to be globally finite-time stable if for any of its solution x(t, x₀), the following statements hold: