Bounds for the Least Laplacian Eigenvalue of a Signed Graph

A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated.     

Symmetry Properties of Positive Solutions of Parabolic Equations on ℝ N : I. Asymptotic Symmetry for the Cauchy Problem

We consider quasilinear parabolic equations on ? ^N satisfying certain symmetry conditions. We prove that bounded positive solutions decaying to zero at spatial infinity are asymptotically radially symmetric about a center. The asymptotic center of symmetry is not fixed a priori (and depends on the solution) but it is independent of time. We also prove a similar theorem on reflectional symmetry.     

Asymptotic Behavior of Solutions to Liquid Crystal Systems in ℝ3

In this paper we study the large time behavior of solutions to a nematic liquid crystal system in the whole space ?³. The fluid under consideration has constant density and small initial data.     

Asymptotic Behavior of Nodal Solutions for Semilinear Elliptic Equationsin R~n

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ，ｔｈｅｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｓ△ｕ＋ｆ（ｕ）＝０（１．１）ｕ（ｘ）→０ａｓ｜ｘ｜→∞（１．２）ｉｎＲｎｗｅｒｅｃｏｎｓｉｄｅｒｅｄｗｉｄｅｌｙ（ｓｅｅ［１］－［７］）．Ｉｎｔｈｅｎｉｃｅｐａｐｅｒｓ［１］ａｎｄ［２］，ｉｔｗａｓｐｒｏｖｅｄｔｈａｔａｎｙｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｏｆ（１．１）ｍｕｓｔｂｅｒａｄｉａｌｉｎｃａｓｅｆ（ｕ）∈Ｃ１＋δ（δ＞０）．Ｔｈｅｒｅｆｏｒｅ，ａｎｙｐｏｓｉｔｉｖｅｓｏｌｕｔｉ…     

Asymptotic Behavior of Solutions to a Class of Systems of Delay Differential Equations

The authors investigate the asymptotic behavior of solutions to a class of systems of delay differential equations. It is shown that every bounded solution of such a class of systems tends to a constant vector as t→∞. Our results improve and extend some corresponding ones already known.     

Oscillatory and Asymptotic Behavior of Solutions for Nonlinear Impulsive Delay Differential Equations

The oscillatory and asymptotic behavior of the solutions for third order nonlinear impulsive delay differential equations are investigated. Some novel criteria for all solutions to be oscillatory or be asymptotic are established, Three illustrative examples are proposed to demonstrate the effectiveness of the conditions.     

Asymptotic Behavior of the Fundamental Solutions for Critical Schrödinger Forms

Journal of Theoretical Probability - Let $$\{X_t\}_{t \ge 0}$$ be a transient $$\alpha $$ -stable process on $${\mathbb {R}}^d$$ and denote by H its generator. We consider the perturbation of the...     

Asymptotic Behavior of Solutions to the Generalized BBM-Burgers Equation

We investigate the asymptotic behavior of solutions of the initial-boundary value problem for the generalized BBM-Burgers equation u_t f(u)_x=u_(xx) u_(xx) on the half line with the conditions u(0, t)=, u-, u(∞,t)=u_ and, u_-相似文献   

Asymptotic Behavior of Bifurcation Branch of Positive Solutions for Semilinear Sturm–Liouville Problems

We consider the nonlinear eigenvalue problem

Symmetry Properties of Positive Solutions of Parabolic Equations on ℝ N : II. Entire Solutions

We consider nonautonomous quasilinear parabolic equations satisfying certain symmetry conditions. We prove that each positive bounded solution u on ? ^N  × (?∞, T) decaying to zero at spatial infinity uniformly with respect to time is radially symmetric around some origin in ? ^N . The origin depends on the solution but is independent of time. We also consider the linearized equation along u and prove that each bounded (positive or not) solution is a linear combination of a radially symmetric solution and (nonsymmetric) spatial derivatives of u. Theorems on reflectional symmetry are also given.     

Liouville Type Theorems for Positive Solutions of Elliptic System in ℝ N

In this paper, by the Alexandrov-Serrin method of moving plane combined with integral inequalities, we prove some new Liouville type results for positive solution of semilinear elliptic system in the whole space ? ^N .     

The Local Asymptotic Behavior of Solutions of Second Order Linear Differential Equations in a Nutshell

1.IntroductionGiven a second order linear differential equation with meromorphic coefficienta(x)y” b(x)y’ c(x)y=0 (1.1)in,a domain D the local analytic theory for such equations is well developed,see e.g.[8].If x_0 is a regular point for(1.1)then the theory advocates to utilize Taylor seriesexpansions of two linearly indepentdent solutions of(1.1).If x_0 is a regular singular pointfor(1.1),Frobenius’method tells us to follow sometimes a laborious procedure which     

Asymptotic Behavior of Solutions of Boundary-Value Problems for the Equation Δu − ku = f in a Layer

For the solutions of boundary-value problems for the equation Δu???ku?=?f in the layer $$ \varPi =\left\{ {\left( {x^{\prime},{x_n}} \right)\in {{\mathbb{R}}^n}|{x}^{\prime}\in {{\mathbb{R}}^{n-1 }},{x_n}\in \left( {a,b} \right)} \right\},\quad -\infty <a<b<+\infty, \quad n\geq 3, $$ one obtains the first term of their asymptotics at infinity.     

Asymptotic and Oscillatory Behavior of Solutions of First Order Neutral Differential Equations

This paper has made researches on first order neutral differential equations with variable coefficients and several deviations. The asymptotic behavior of nonoscillatory solutions of the equations are discussed. Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained. The relevent results in [1—3] are improved and generalized .     

Asymptotic Behavior of Solutions of Certain Delay Differential Equations with Periodic Coefficients

§1 Introduction In [1], we have discussed the asymptotic behavior and structure of solutions of the linear delay differential equation (1.1) (r>0 is a real constant), and have obtained the following result: If p(t)=const., or p(t)>0 and integral from n=t to t+r(p(s)ds≥1) , then any solution x(t) of (1.1) can be expressed as     

The Asymptotic Behavior of Solutions of Some Doubly Degenerate Nonlinear Parabolic Equations

Ｔｈｅ　Ａｓｙｍｐｔｏｔｉｃ　Ｂｅｈａｖｉｏｒ　ｏｆ　Ｓｏｌｕｔｉｏｎｓ　ｏｆ　Ｓｏｍｅ　Ｄｏｕｂｌｙ　Ｄｅｇｅｎｅｒａｔｅ　Ｎｏｎｌｉｎｅａｒ　Ｐａｒａｂｏｌｉｃ　ＥｑｕａｔｉｏｎｓＹａｎｇＪｉｎｓｈｕｎ（杨金顺）（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉ...     

Asymptotic Behavior of Oscillatory Solutions of Forced Nonlinear Neutral Delay Differential Equations

§1.　IntroductionThispaperisconcernedwiththeasymptoticbehavioroftheoscillatorysolutionsofnonlin-earforcedneutraldelaydifferentialequationsoftheform[x(t)-∑mi=1pi(t)x(t-τi)]′ ∑nj=1qj(t)f(x(t-σj))=r(t),　t≥t0,(1)wherepi,qj,r∈C([t0,∞),R),τi,σj≥0,i=1,2,…,m;j=1,2,…,n,f∈C(R,R),xf(x)>0forx≠0.Whenpi(t)≡0,i=1,2,…,m,Eq.(1)reducestox(t) ∑nj=1qj(t)f(x(t-σj))=r(t),　t≥t0,(2)whoseasymptoticbehaviorofallsolutionshasbeenstudiedinJ.R.Yan[5].Whenr(t)≡0,f(x)≡xandm=n=1,Eq.(1)reducesto[…     

Asymptotic of the Solutions of the Initial Boundary Value Problem for the Diffusion Equations for Semiconductors（Ⅱ）

The paper deal with the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.     

A Note on the Lanczos Algorithm for Skew Symmetric Eigenvalue Problem

In[1]and[2]we disscussed the eigenvalue problem for real normal matrices and the eigenvalue problem for normal matrices in generalized inner product, respectively.In this note we will show that if matrix A is a skew symmetric. matrix (c.f.[1]) or matrix G is a B-skew symmetric matrix(c.f.[2]), then the Lanczos algorithm with respect to A or to G can be implemented by real arithmatic and is even simpler than that with respect to a symmetric matrix or to a B-symmetric matrix respectively.