UNIFORM STABILITY AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF 2-DIMENSIONAL MAGNETOHYDRODYNAMICS EQUATIONS

ＵＮＩＦＯＲＭＳＴＡＢＩＬＩＴＹＡＮＤＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＳＯＬＵＴＩＯＮＳＯＦ２－ＤＩＭＥＮＳＩＯＮＡＬＭＡＧＮＥＴＯＨＹＤＲＯＤＹＮＡＭＩＣＳＥＱＵＡＴＩＯＮＳＺＨＡＮＧＬＩＮＧＨＡＩＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕ...     

A CHARACTERIZATION OF THE SOLUTIONS OF p－ORDER FEIGENBAUM＇S FUNCTIONAL EQUATION WITH TOPOLOGICAL ENTROPY 0

ＡＣＨＡＲＡＣＴＥＲＩＺＡＴＩＯＮＯＦＴＨＥＳＯＬＵＴＩＯＮＳＯＦｐ－ＯＲＤＥＲＦＥＩＧＥＮＢＡＵＭ＇ＳＦＵＮＣＴＩＯＮＡＬＥＱＵＡＴＩＯＮＷＩＴＨＴＯＰＯＬＯＧＩＣＡＬＥＮＴＲＯＰＹ０（廖公夫）￥ＬｉａｏＧｏｎｇｆｕ（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｊｉ...     

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR A CLASS OF THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATION

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＴＨＥＳＹＳＴＥＭＳＯＦＭＩＸＥＤＭＯＮＯＴＯＮＥＯＰＥＲＡＴＯＲＥＱＵＡＴＩＯＮＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＨＥＮＰＥＩＬＯＮＧ...     

MAJOR－EFFICIENT SOLUTIONS AND WEAKLY MAJOR－EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING

ＭＡＪＯＲ－ＥＦＦＩＣＩＥＮＴＳＯＬＵＴＩＯＮＳＡＮＤＷＥＡＫＬＹＭＡＪＯＲ－ＥＦＦＩＣＩＥＮＴＳＯＬＵＴＩＯＮＳＯＦＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧ￥ＨＵＹＵＤＡ（Ｄｅｐｔ．ｏｆＡｐｐｌ．Ｍａｔｈ．，ＳｈａｎｇｈａｉＪｉａｏＴｏｎ...     

LARGE－TIME BEHMIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGHPOROUS MEDIA

ＬＡＲＧＥ－ＴＩＭＥＢＥＨＭＩＯＲＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＣＯＭＰＲＥＳＳＩＢＬＥＡＤＩＡＢＡＴＩＣＦＬＯＷＴＨＲＯＵＧＨＰＯＲＯＵＳＭＥＤＩＡ￥ＸＩＡＯＬＩＮＧ（Ｌ．ＨＳＩＡＯ）Ｄ．ＳＥＲＲＥ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔ...     

A NOTE OF UNIFORM EXPONENTIAL STABILIZATION FOR NONCONTRACTIVE SEMIGROUPS UNDER COMPACT PERTURBATION

ＡＮＯＴＥＯＦＵＮＩＦＯＲＭＥＸＰＯＮＥＮＴＩＡＬＳＴＡＢＩＬＩＺＡＴＩＯＮＦＯＲＮＯＮＣＯＮＴＲＡＣＴＩＶＥＳＥＭＩＧＲＯＵＰＳＵＮＤＥＲＣＯＭＰＡＣＴＰＥＲＴＵＲＢＡＴＩＯＮＳｏｎｇＧｕｏｚｈｕ（宋国柱）（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｎａｎｊｉｎｇ...     

ASYMPTOTIC STABILITY FOR A CLASS OF NONAUTONOMOUS NEUTRAL DIFFERENTIAL EQUATIONS

ＡＳＹＭＰＴＯＴＩＣＳＴＡＢＩＬＩＴＹＦＯＲＡＣＬＡＳＳＯＦＮＯＮＡＵＴＯＮＯＭＯＵＳＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ＊＊ＹＵＪＩＡＮＳＨＥ＊ＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕｌｙ４，１９９５．ＲｅｖｉｓｅｄＭａｒｃｈ２...     

ON THE UPPER ESTIMATES OF FUNDAMENTAL SOLUTIONS OF PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS

ＯＮＴＨＥＵＰＰＥＲＥＳＴＩＭＡＴＥＳＯＦＦＵＮＤＡＭＥＮＴＡＬＳＯＬＵＴＩＯＮＳＯＦＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳＯＮＲＩＥＭＡＮＮＩＡＮＭＡＮＩＦＯＬＤＳ￥ＬＩＪＩＡＹＵ；ＳＨＡＯＸＩＮ（ＤｅｐａｒｔｍｅｌｌｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ａ...     

ALMOST PERIODIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

ＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＰＩＥＣＥＷＩＳＥＣＯＮＳＴＡＮＴＡＲＧＵＭＥＮＴＹＵＡＮＲＯＮＧＨＯＮＧＪＩＡＬＩＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕ...     

ASYMPTOTIC BEHAVIOR OF NONOSCILLATORY SOLUTIONS OF A SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

ＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＮＯＮＯＳＣＩＬＬＡＴＯＲＹＳＯＬＵＴＩＯＮＳＯＦＡＳＥＣＯＮＤＯＲＤＥＲＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ（孟繁伟）曲阜师范大学，邮编：２７３１６５ＭｅｎｇＦａｎｗｅｉ（ＱｕｆｕＮ...     

Existence of C1-solutions to Certain Non-uniformly Degenerate Elliptic Equations

We are concerned with the Dirichlet problem of {div A(x, Du) + B(z) = 0 \qquad in Ω u= u_0 \qquad \qquad on ∂ Ω Here Ω ⊂ R^N is a bounded domain, A(x, p) = (A¹ (x, p), ... >A^N (x, p}) satisfies min{|p|^{1+α}, |p|^{1+β}} ≤ A(x, p) ⋅ p ≤ α_0(|p|^{1+α}+|p|^{1+β}) with 0 < α ≤ β. We show that if A is Lipschitz, B and u_0 are bounded and β < max {\frac{N+2}{N}α + \frac{2}{N},α + 2}, then there exists a C¹-weak solution of (0.1).     

Bounded solutions in a T-shaped waveguide and the spectral properties of the Dirichlet ladder

The Dirichlet problem is considered on the junction of thin quantum waveguides (of thickness h ? 1) in the shape of an infinite two-dimensional ladder. Passage to the limit as h → +0 is discussed. It is shown that the asymptotically correct transmission conditions at nodes of the corresponding one-dimensional quantum graph are Dirichlet conditions rather than the conventional Kirchhoff transmission conditions. The result is obtained by analyzing bounded solutions of a problem in the T-shaped waveguide that the boundary layer phenomenon.     

Remarks on the Shape of Least-energy Solutions to a Semilinear Dirichlet Problem

Structure of least-energy solutions to singularly perturbed semilinear Dirichlet problem ε²Δu - u^α + g(u) = 0 in Ω,u = 0 on ∂Ω, Ω ⊂ ⋅R^N a bounded smooth domain, is precisely studied as ε → 0^+, for 0 < α < 1 and a superlinear, subcritical nonlinearity g(u). It is shown that there are many least-energy solutions for the problem and they are spike-layer solutions. Moreover, the measure of each spike-layer is estimated as ε → 0^+ .     

Sharp estimates for intrinsic ultracontractivity on C 1,α-domains

Let be the first Dirichlet eigenfunction on a connected bounded C ^1,α-domain in and the corresponding Dirichlet heat kernel. It is proved that where λ₂ > λ₁ are the first two Dirichlet eigenvalues. This estimate is sharp for both short and long times. Bounded Lipschitz domains, elliptic operators on manifolds, and a general framework are also discussed. Supported in part by Creative Research Group Fund of the National Foundation of China (no. 10121101), the 973-Project in China and RFDP(20040027009).     

On the mean value of the generalized Dirichlet <Emphasis Type="Italic">L</Emphasis>-functions

Let q ⩾ 3 be an integer, let χ denote a Dirichlet character modulo q. For any real number a ⩾ 0 we define the generalized Dirichlet L-functions

Smoluchowski-Kramers approximation for a general class of SPDEs

We prove that the so-called Smoluchowski-Kramers approximation holds for a class of partial differential equations perturbed by a non-Gaussian noisy term. Namely, we show that the solution of the one-dimensional semi-linear stochastic damped wave equations , u(0) = u₀, u_t (0) = v₀, endowed with Dirichlet boundary conditions, converges as the parameter μ goes to zero to the solution of the semi-linear stochastic heat equation , u(0) = u₀, endowed with Dirichlet boundary conditions. Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday     

Positive solutions to singular semipositone boundary value problems of second order coupled differential systems

We establish the existence of positive solutions for the second order singular semipositone coupled Dirichlet systems $$\left\{ \begin{aligned} &x{''} +f_1 \bigl(t,y(t)\bigr)+e_1(t)=0, \\ &y{''} +f_2\bigl(t,x(t) \bigr)+e_2(t)=0, \\ &x(0)=x(1)=0,\qquad y(0)=y(1)=0. \end{aligned} \right. $$ The proof relies on Schauder’s fixed point theorem.     

Oscillatory Perturbations of Linear Problems at Resonance

This paper is concerned with a study of bounded perturbations of resonant linear problems. It follows from our results that for certain types of bounded domains Ω ? Rⁿ, n ≥ 2, the Dirichlet problem $\matrix{\Delta u+\lambda_{1}u+g(u)=h(x),\ \ \ x\in\Omega\cr \quad\quad\quad\quad\quad\quad u=0,\ \ \ x\in\partial\Omega,}$ has infinitely many positive solutions, in case λ₁ is the principal eigenvalue of ?Δ subject to trivial Dirichlet boundary conditions, g is a nontrivial periodic nonlinearity of zero mean and ∫_03A9h(x)?(x)dx = 0, where ? is an eigenfunction corresponding to λ₁.     

Existence of multiple solutions for semilinear elliptic equations in the annulus

The existence of radial solutions of Δu ＋ λg（｜x｜）f（u） = 0 in annuli with Dirichlet（Dirichlet/Neumann） boundary conditions is investigated.It is proved that the problems have at least two positive radial solutions on any annulus if f is superlinear at 0 and sublinear at ∞.     

有限重数的Dirichlet移位

In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n ＋ 1 （n ≥ 0） if and only if its symbol is c zn＋1 for some constant c. The result is very different from the cases of both the Bergman space and the Hardy space.