HOLDER CONTINUITY AND DIFFERENTIABILITY ON CONVERGING SUBSEQUENCES

It is shown that an arbitrary function from D ?Rn to Rm will become C0,α-continuous in almost every x ∈ D after restriction to a certain subset with limit point x. For n ≥ m differentiability can be ob...     

RIGIDITY THEOREMS OF CLIFFORD TORUS

In this article, we prove that the Clifford torus S1(1-r2~(1/2)) × Sn-1(r) is the only closed hypersurface in the unit sphere Sn+1(1) with infinite fundamental group, which satisfy r2 ≥ (n-1)/n, RicM ≤ C-(H), and S ≤ S+(H). Moreover, we give a characterization of Clifford torus S1(1-r2~(1/2)) × Sn-1(r) with r2 = 2(n-1)+nH2±|H| n2H2+4(n-1)(1/2)/2n(1+H2) .     

SOME PROPERTIES OF COMMUTING AND ANTI-COMMUTING m-INVOLUTIONS

We define an m-involution to be a matrix K ∈ Cn×n for which Km =I.In this article,we investigate the class Sm (A) of m-involutions that commute with a diagonalizable matrix A ∈ Cn×n.A number of basic p...     

MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID

This article is concerned with the existence of maximal attractors in Hi(i=1,2,4) for the compressible Navier-Stokes equations for a polytropic viscous heat conduc-tive ideal gas in bounded annular domains Ωn in Rn(n =2,3).One of the important features is that the metric spaces H(1),H(2),and H(4) we work with are three incomplete metric spaces,as can be seen from the constraints θ0 and u0,with θ and u being absolute temperature and specific volume respectively.For any constants δ1,δ2,···,δ8 verifying some conditions,a sequence of closed subspaces Hδ(i)H(i)(i = 1,2,4) is found,and the existence of maximal(universal) attractors in Hδ(i)(i = 1,2,4) is established.     

PHASE RETRIEVAL OF TIME-LIMITED SIGNALS

The problem of reconstructing a signal ψ(x) from its magnitude |ψ(x)| is of considerable interest to engineers and physicists.This article concerns the problem of determining a time-limited signal f with period 2π when |f(eix)| is known for x ∈ [-π,π].It is shown that the conditions |g(eix)| = |f(eix)| and |g(ei(x+b))-g(eix)| = |f(ei(x+b))-f(eix)|,b = 2π,together imply that either g = wf or g = vf,where both w and v have period b.Furthermore,if 2bπ is irrational then the functions w and v reduce to some constants c1 and c2,respectively;if 2bπ is rational then w takes the form w=eiαB1(eix)B2(eix) and v takes the form ei(x2πN/b+α)B1(eix)B2(eix),where B1 and B2 are Blaschke products.     

MULTIPLE AND SIGN-CHANGING SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATION WITH CRITICAL POTENTIAL AND CRITICAL PARAMETER

Some embedding inequalities in Hardy-Sobolev space are proved.Furthermore,by the improved inequalities and the linking theorem,in a new k-order Sobolev-Hardy space,we obtain the existence of sign-changing solutions for the nonlinear elliptic equation {-△(k)u:=-△u-(((N-2)2)/4)U/︱X︱2-1/4 sum from i=1 to(k-1) u/(︱x︱2(In(i)R/︱x︱2))=f(x,u),x ∈Ω,u=0,x ∈Ω,where 0 ∈ΩBa(0)RN,N≥3,ln(i)=i éj=1 ln(j),and R=ae(k-1),where e(0)=1,e(j) = ee(j-1) for j≥1,ln(1)=ln,ln(j)=ln ln(j-1) for j≥2.Besides,positive andnegative solutions are obtained by a variant mountain pass theorem.     

LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL＊

This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear Schr(o)dinger equation with a Stark potential.By using the variational characterization of corresponding gro...     

Complexity of asymptotic behavior of solutions for the porous medium equation with absorption

In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption u t-u m + γup = 0, where γ≥ 0, m 1 and p m + 2/N . We will show that if γ = 0 and 0 μ 2N/(N(m-1)+2), or γ 0 and 1/(p-1)μ2N/(N(m-1)+2), then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S (R N ), there exists an initial-value u0 ∈C(RN) with lim x →∞ u 0 (x) = 0 such that φ is an ω-limit point of the rescaled solutions t μ/2 u(t β·, t), where β =[2-μ(m-1)]/4 .     

THE SHARP ESTIMATE OF THE THIRD HOMOGENEOUS EXPANSION FOR A CLASS OF STARLIKE MAPPINGS OF ORDER α ON THE UNIT POLYDISK IN Cn

In this article,first,a sufficient condition for a starlike mapping of order α f(x) defined on the unit ball in a complex Banach space is given. Second,the sharp estimate of the third homogeneous expan...     

PERTURBATIONS OF ZEROS OF SOLUTIONS TO SECOND ORDER DIFFERENTIAL EQUATIONS WITH POLYNOMIAL COEFFICIENTS＊

Let P(z) and (P)(z) be polynomials of the same degree. We consider the equations u" =P(z)u and (u)" =(P)(z)(u) (z ∈ C) whose solutions are u(z) and (u)(z),respectively.Let zk(u) and zk((u)),k =1,2,…,be...     

Fountain theorem over cones and applications

In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-pu = λ|u|q-2u + μ|u| γ-2 u, x ∈Ω,u = 0, x ∈Ω,(1)to show that problem (1) possesses infinitely many solutions, where 1 p N, 1 q p γ, ΩRN is a smooth bounded domain and λ, μ∈ R.