作者机构：
Huazhong Normal Univ, Dept Math, Wuhan 430070, Peoples R China.;Chinese Acad Sci, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China.;Tsing Hua Univ, Dept Appl Math, Beijing 100084, Peoples R China.;Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China.;[Wei, B] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA.
通讯机构：
[Wei, B] G;Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA.
关键词：
1-tough;Hamiltonian graph;Triangle-free
摘要：
A graph G is called triangle-free if G has no induced K3 as a subgraph. We set σ3=min{∑i=13d(vi)|{v1,v2,v3} is an independent set of vertices in G}. In this paper, we show that if G is a 1-tough and triangle-free graph of order n with n⩽σ3, then G is hamiltonian.
期刊：
Journal of Mathematical Analysis and Applications,2002年276(2):497-515 ISSN：0022-247X
通讯作者：
Yao, ZA
作者机构：
[Yao, ZA] Zhongshan Univ, Dept Math, Guangzhou 510275, Peoples R China.;Cent China Normal Univ, Dept Math, Wuhan 430070, Peoples R China.;City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China.
摘要：
In this paper, we consider the asymptotic behavior of solution for the Cauchy problem for p-system with relaxation nu(t) - u(x) = 0, u(t) + p(nu)(x) = 1/epsilon(f (nu) - u), (E) with initial data (nu,u)(x,0)=(nu(0)(x),u(0)(x)) --> (nu(0), u+/-), as x --> +/-infinity. (I) By applying the elementary energy method and the Green function method for the parabolic equation, we obtain the L-P-convergence rate to the diffusion waves for the Cauchy problem (E), (I). (C) 2002 Elsevier Science (USA). All rights reserved.
期刊：
Journal of Mathematical Analysis and Applications,2002年271(1):155-174 ISSN：0022-247X
通讯作者：
Deng, YB
作者机构：
[Peng, SJ; Deng, YB] Huazhong Normal Univ, Dept Math, Lab Nonlinear Anal, Wuhan 430079, Peoples R China.
通讯机构：
[Deng, YB] H;Huazhong Normal Univ, Dept Math, Lab Nonlinear Anal, Wuhan 430079, Peoples R China.
关键词：
Neumann problem;Positive solution;Supersolution and subsolution
摘要：
In this paper, we study the existence and nonexistence of multiple positive solutions for the inhomogeneous Neumann boundary value problem Deltau + u(P) - lambdau = 0, with Dgammau = phi(x), under some assumptions on the boundary partial derivativeOmega and the function phi(x). For phi(x) greater than or equal to 0, phi(x) not equivalent to 0, phi(x) is an element of C-alpha((&UOmega;) over bar), it is shown that there exists a constant lambda* > 0 such that problem (*) possesses at least two positive solutions if lambda is an element of (lambda*, infinity) and at least one positive solution if lambda = lambda*. Furthermore, there are no positive solutions for problem (*) if lambda is an element of (-infinity, lambda*). (C) 2002 Elsevier Science (USA). All rights reserved. [References: 10]
期刊：
Computers & Mathematics with Applications,2002年44(3-4):439-444 ISSN：0898-1221
通讯作者：
Yan, GZ
作者机构：
[Yan, GZ] Cent China Normal Univ, Dept Math, Wuhan, Peoples R China.
通讯机构：
[Yan, GZ] C;Cent China Normal Univ, Dept Math, Wuhan, Peoples R China.
关键词：
Far field pattern;Helmholtz equation;Inverse scattering;Transmission problem;Uniqueness
摘要：
A method for studying the inverse obstacle scattering problem with transmission boundary condition was introduced. The transmission boundary was uniquely determined by the far field pattern. Results showed that the continuity of pressure and normal velocity across interface lead to the transmission condition.
摘要：
This paper is concerned with a maximum principle of optimal control problems governed by some parabolic differential equations which could be non-well-posed. Both an integral-type state constraint and a two-point boundary (time variable) state constraint are considered.
摘要：
In this paper, we study the Euler-Poisson equations governing gas motion under self-gravitational force. We are interested in the evolution of the gaseous stars, for which the density function has compact support. We establish existence theory for the stationary solutions and describe the behavior of the solutions near the vacuum boundary. The boundary behavior thus obtained agrees with the physical boundary condition proposed and studied in [L, LY] for both Euler equations with damping and the Euler-Poisson equations. Existence, non-existence, uniqueness and instability of the stationary solutions with vacuum are also discussed in terms of the adiabatic exponent and the entropy function. And the phenomena of the blowup, that is, the collapsing of the star to a single point with finite mass, as well as the drifting of part of the star to infinity in space are also studied and shown to agree with the conjecture from the physical considerations.
作者机构：
[Wang, GS] Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, G.] D;Department of Mathematics, Huazhong Normal University, China
关键词：
maximum principle;optimal control problems;finite codimension;state constraint;approximate controllability
摘要：
This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations. The maximum principle and some kind of approximate controllability are studied.
摘要：
Optimal control problem governed by y′ + Ay + f(t,y) = Bu in (0,T), with state constraint (y(t 0),…,y(t n ) ∈ S, where is a convex and closed subset, 0 = t 0 < t 1 < ċ < t n = T, B is a linear operator from a controller space U into a state H and A is a linear operator in H. Some applications are given.
作者机构：
[Liang, ZJ; Sleeman, BD] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Liang, Z.] D;Department of Mathematics, Central China Normal University, China
关键词：
homogeneous vector field;invariant cone
摘要：
In this paper, the authors investigate the invariant cones of quadratic homogeneous polynomial vector fields in three variables. Necessary and sufficient conditions for the existence of non-isolated invariant closed cones are obtained by the algebraic expressions in terms of the coefficients of certain quadratic homogeneous polynomials.
摘要：
In this paper, we have obtained the necessary and sufficient condition for the set of points at infinity on the plane R2 to be a periodic orbit which is called an equatorial periodic orbit of a planar vector field X(x), and the formulae about the multiplicity of the equatorial periodic orbit of X(x). We have also proved that the main result of [9] is erroneous with regard to the formulae.
作者机构：
[Zhu, CJ] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;[Zhu, CJ] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China.
通讯机构：
[Zhu, CJ] C;City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China.
摘要：
The limit behavior of the approximate solutions to the Cauchy problem for the general 2 ×2 nonlinear hyperbolic systems of conservation laws is investigated. This system is called strictly hyperbolic in a set if the Jacobian has two real and distinct eigenvalues. When the system is strictly hyperbolic and genuinely nonlinear in the set under consideration, the convergence of the approximate solutions is proven by the method of compensated compactness.
期刊：
Communications in Partial Differential Equations,2001年26(5-6):965-981 ISSN：0360-5302
通讯作者：
Yang, T
作者机构：
City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China.;Zhongshan Univ, Dept Math, Canton 510275, Peoples R China.;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;[Yang, T] City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Kowloon, Hong Kong, Peoples R China.
通讯机构：
[Yang, T] C;City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Kowloon, Hong Kong, Peoples R China.
摘要：
In this paper, we discuss the anisotropic static Landau-Lifshitz equations. We obtain maximum principles and existence results for the small solutions to the Dirichlet problems and the initial-boundary value problems of the corresponding evolution equations. We also construct multiple large smooth solutions in the two dimensions. These problems are dealt with from the viewpoint of harmonic maps with potential. (C) 2001 Academic Press. [References: 18]
期刊：
Journal of Mathematical Biology,2001年43(3):268-290 ISSN：0303-6812
通讯作者：
Xiao, DM
作者机构：
[Xiao, DM] Cent China Normal Univ, Dept Math, Wuhan 430079, Hebei, Peoples R China.;Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada.
通讯机构：
[Xiao, DM] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Hebei, Peoples R China.
关键词：
Attractor;Critical point of higher order;Limit cycle;Predator-prey system;Ratio-dependent response
摘要：
Recently, ratio-dependent predator-prey systems have been regarded by some researchers to be more appropriate for predator-prey interactions where predation involves serious searching processes. However, such models have set up a challenging issue regarding their dynamics near the origin since these models are not well-defined there. In this paper, the qualitative behavior of a class of ratio-dependent predator-prey system at the origin in the interior of the first quadrant is studied. It is shown that the origin is indeed a critical point of higher order. There can exist numerous kinds of topological structures in a neighborhood of the origin including the parabolic orbits, the elliptic orbits, the hyperbolic orbits, and any combination of them. These structures have important implications for the global behavior of the model. Global qualitative analysis of the model depending on all parameters is carried out, and conditions of existence and non-existence of limit cycles for the model are given. Computer simulations are presented to illustrate the conclusions.
作者机构：
[Wang, GS] Huazhong Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.;Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China.;Lanzhou Univ, Dept Math, Lanzhou 730000, Peoples R China.
通讯机构：
[Wang, GS] H;Huazhong Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
关键词：
Pontryagin's maximum principle;semilinear elliptic equations;minimal positive solution;control;state constraint
摘要：
The optimal control problem governed by a semilinear elliptic differential state equation is studied. The controlled system is not governed by a monotone operator and the control entered nonlinearity. To get Pontryagin's maximum principle, the Ekeland's variational principle and a method based on penalization of state constraints are used.
期刊：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2001年11(8):2123-2131 ISSN：0218-1274
通讯作者：
Xiao, DM
作者机构：
[Xiao, DM] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.;Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada.
通讯机构：
[Xiao, DM] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
摘要：
In this paper we study the qualitative behavior of a predator-prey system with nonmonotonic functional response. The system undergoes a series of bifurcations including the saddle-node bifurcation, the supercritical Hopf bifurcation, and the homoclinic bifurcation. For different parameter values the system could have a limit cycle or a homoclinic. loop, or exhibit the so-called "paradox of enrichment" phenomenon. In the generic case, the model has the bifurcation of cusp-type codimension two (i.e. the Bogdanov-Takens bifurcation) but no bifurcations of codimension three.
期刊：
Journal of Differential Equations,2001年176(2):494-510 ISSN：0022-0396
通讯作者：
Xiao, DM
作者机构：
[Xiao, DM] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.;Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada.
通讯机构：
[Xiao, DM] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
摘要：
A delayed predator-prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by Faria and Magalhaes. The bifurcation analysis of the model indicates that there is a Bogdanov-Takens singularity for any time delay value. A versal unfolding of the model at the Bogdanov-Takens singularity is obtained. On the other hand, it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit Hopf bifurcation as the time delay passes through some critical values. (C) 2001 Academic Press.
