A New Third S.N.Bernstein Interpolation Polynomial

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｋｎｏｗｎｔｈａｔｉｓｎｏｔｐｏｓｓｉｂｌｅｔｈａｔｔｈｅＬａｇｒａｎｇｅｉｎｔｅｒｐｏｌａｔｉｏｎｐｏｌｙｎｏｍｉａｌｓｃｏｎｖｅｒｇｅｕｎｉ－ｆｏｒｍｌｙｔｏｆ（ｘ）ｆｏｒａｌｌｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎｓｆ（ｘ）ｏｎ［－１，１］．Ａｓａｒｅｓｕｌｔ，ｏｎｅｃａｎｕｓｅｖａｒｉｏｕｓｗａｙｓｔｏｃｈａｎｇｅｔｈｅＬａｇｒａｎｇｅｉｎｔｅｒｐｏｌａｔｉｏｎｐｏｌｙｎｏｍｉａｌｓｕｃｈｔｈａｔｔｈｅｙｕｎｉｆｏｒｍｌｙｃｏｎｖｅｒｇｅｔｏａｌｌｃｏｎ…     

THE MATHEMATICAL BEHAVIOR OF A NONAUTONOMOUS VOLTERRA PREDATOR-PREY SYSTEM WITH UNDERCROWDING EFFECT

１ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｃｏｎｓｉｄｅｒｔｈｅＶｏｌｔｅｒａｐｒｅｄａｔｏｒｐｒｅｙｍｏｄｅｌｗｉｔｈＬｏｇｉｓｔｉｃｐｒｅｙｇｒｏｗｔｈｒａｔｅ：ｘ＝ａｘ（Ｋ－ｘ）－ｂｘｙ，ｙ＝－ｃｙ＋ｄｘｙ－αｙ２．（１．１）Ｔｈｉｓｍｏｄｅｌｈａｓａｕ...     

A CRITERION OF THE NON-EXISTENCE OF PERIODIC SOLUTIONS FOR A GENERALIZED LINARD SYSTEM AND ITS APPLICATIONS

§１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｕｒｐｏｓｅｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｇｉｖｅａｎｅｗｃｒｉｔｅｒｉｏｎｏｆｔｈｅｎｏｎ－ｅｘｉｓｔｅｎｃｅｏｆｐｅｒｉｏｄｉｃｓｏ－ｌｕｔｉｏｎｓｆｏｒａｎｏｎｌｉｎｅａｒｄｉｆｅｒｅｎｔｉａｌｓｙｓｔｅｍｏ...     

EXISTENCE OF STABLE EQUILIBRIUM FOR A CLASS OF MULTI-SPECIES ECOSYSTEM

１ＩｎｔｒｏｄｕｃｔｉｏｎＳｃｈｅｏｎｅｒｈａｓｓｔｕｄｉｅｄｔｗｏｓｐｅｃｉｅｓｅｃｏｓｙｓｔｅｍ：ｘｉ＝ｒｉｘｉ（ｌｉｅｉ＋ｘｉ－γｉ１ｘｉ－γｉ２ｘ２－ｃｉ）（ｉ＝１，２）（１）ｗｈｅｒｅｒｉ，γｉｊ，ｅｉ，ｌｉ＞０（ｉ，ｊ＝１，２）．Ｕｎｄｅ...     

A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ１９０８，Ｅ．Ｌａｎｄａｕｉｎｔｒｏｄｕｃｅｄｔｈｅｆｏｌｌｏｗｉｎｇｗｅｌｌｋｎｏｗｎｓｅｑｕｅｎｃｅｏｆｏｐｅｒａｔｏｒｓ［１］Ｌｎ［ｆ（ｔ）；ｘ］＝Ｋｎ∫１－１ｆ（ｔ）［１－（ｔ－ｘ）２］ｎｄｔ，　　　　（１．１）ｗｈｅｒｅ　　　　　Ｋｎ＝［∫１｛－１（１－ｔ２）ｎｄｔ］－１～ｎπ　　（ｎ→∞）．（１．１）ｗａｓｕｓｅｄｉｎｔｈｅｐｒｏｏｆｏｆｔｈｅＷｅｉｅｒｓｔｒａｓｓＴｈｅｏｒｅｍ．Ｓｉｎｃｅｔｈｅｎ，ｔｈｅａｐｐｒｏｘｉｍａｔｉｏｎｐｒｏｐ－ｅｒｔ…     

THE VARIATION OF INVARIANT LINES AND LIMIT CYCLES FOR A QUADRATIC DIFFERENTIAL SYSTEM

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｒｅａｌｑｕａｄｒａｔｉｃｄｉｆｅｒｅｎｔｉａｌｓｙｓｔｅｍｘ＝－ｙ＋δｘ－４ｘ２＋３ｘｙ＋１３ｙ２ｙ＝ｘ（１－１３ｘ－ｙ）．（１）Ｆｉｒｓｔ，ｆｏｒｃｏｎｖｅｎｉｅｎｃｅ，ｗｅｄｅｎｏｔｅｔｈｅｔｗｏ...     

A MATHEMATICAL MODEL OF A CLASS OF AUTOCATALYTIC CHEMICAL REACTION

Ｂｙｆｏｌｏｗｉｎｇｍｅｃｈａｎｉｓｍ：ＡａαＸ，ＣｃαＹ，Ｂ＋ＸｂαＹ＋Ｄ，Ｘ＋Ｙｅα３Ｙ，ＹｆαＦ，ＸλαＦ，ａｒｔｉｃｌｅ［１］ｏｂｔａｉｎｅｄｔｈｅｆｏｌｏｗｉｎｇｓｙｓｔｅｍ：ｘ＝ａ－ｂｘ－ｅｘｙ２－λｘ，ｙ＝ｂｘ＋ｅｘｙ２－ｆｙ＋ｃ．（１...     

A Com binatorial Approach for Topological Classification of Graphlike M anifolds

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｔｏｐｏｌｏｇｉｃａｌｃｌａｓｓｉｆｉｃａｔｉｏｎａｎｄｅｎｕｍｅｒａｔｉｏｎｐｒｏｂｌｅｍｏｎｇｒａｐｈｌｉｋｅｍａｎｉｆｏｌｄｓｗａｓｒａｉｓｅｄｉｎ［１］．Ｓｅｖｅｒａｌｒｅｓｕｌｔｓｗｉｔｈｒｅｓｐｅｃｔｔｏｓｐｅｃｉａｌｇｒａｐｈｌｉｋｅｍａｎｉｆｏｌｄｓｗｅｒｅｇｉｖｅｎｉｎ［１～８］．Ｗｅｓｈａｌｌｓｔｕｄｙｔｈｉｓｐｒｏｂｌｅｍｉｎａｖｉｅｗｐｏｉｎｔｏｆｐｕｒｅｃｏｍｂｉｎａｔｏｒｉｃｓ．Ｉｎｆａｃｔ，ａｎｅｗｔｙｐｅｏｆｅｎｕｍｅｒａ－ｔ…     

GLOBAL ATTRACTOR OF A SPATIALLY DISCRETIZED REACTION-DIFFUSION SYSTEM WITH HAMILTONIAN STRUCTURE

１ＨａｍｉｌｔｏｎｉａｎＳｔｒｕｃｔｕｒｅｉｎＲｅａｃｔｉｏｎ－ＤｉｆｕｓｉｏｎｓｙｓｔｅｍＣｏｎｓｉｄｅｒａｓｙｓｔｅｍｏｆｒｅａｃｔｉｏｎ－ｄｉｆｕｓｉｏｎｅｑｕａｔｉｏｎｓｕｔ＝ｕｘｘ＋ｆ（ｕ，ｖ）ｖｔ＝ｖｘｘ＋ｇ（ｕ，ｖ）｛（１．１）ｗｈｅｒ...     

ON A PERIODIC DELAY LOGISTIC TYPE POPULATION MODEL

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｏｗｉｎｇｐｅｒｉｏｄｉｃｄｅｌａｙＬｏｇｉｓｔｉｃｔｙｐｅｐｏｐｕｌａｔｉｏｎｄＮ（ｔ）ｄｔ＝ｒ（ｔ）Ｎ（ｔ）１－ｘ（ｔ－τ（ｔ）Ｋ（ｔ）θ，（１．１）ｗｉｔｈａｎｉｎｉｔｉａｌｃｏｎｄｉｔｉｏ...     

Minimization of integral functionals depending on lipschitz domains

In this paper is solved a minimization problem for what is essentially an integral functional depending on domains which verify an uniform cone property with a fixed parameter θ by extending the techniques land results of O. Caligaris and P. Oliva ‘1’ for convex sets. A Dirichlet condition and an obstacle are considered.     

微分方程递归算子的一种推广

微分方程的多数重要的递归算子都是积微分算子·　在试图获得整个对称族时人们常常遇到困难·　有时甚至由于缺乏精确性而导致伪对称·　本文给出递归算子一种推广，其在某种程度上消除了这些问题·　文中还给出了若干重要例子说明这种推广及其重要性·     

Quasistatic and dynamic problems in viscoplasticity theory—non‐linearities with power growth

We find a common abstract formulation of the quasistatic and dynamic problems from viscoplasticity theory. Based on this formulation we show existence and uniqueness of the solution to this abstract problem by choosing appropriate spaces and by reducing the problem to an evolution equation, which can be treated by the general theory of monotone operators in Hilbert space. Our proof is valid for non‐linearities in the constitutive equation with power law growth. Copyright © 2004 John Wiley & Sons, Ltd.     

Ergodicity for Nonlinear Stochastic Equations in Variational Formulation

This paper is concerned with nonlinear partial differential equations of the calculus of variation (see [13]) perturbed by noise. Well-posedness of the problem was proved by Pardoux in the seventies (see [14]), using monotonicity methods. The aim of the present work is to investigate the asymptotic behaviour of the corresponding transition semigroup P_t. We show existence and, under suitable assumptions, uniqueness of an ergodic invariant measure ν. Moreover, we solve the Kolmogorov equation and prove the so-called "identite du carre du champs". This will be used to study the Sobolev space W^1,2(H,ν) and to obtain information on the domain of the infinitesimal generator of P_t.     

一个非连续增算子不动点定理及其应用

本文在无限区间上给出了一个新的非连续增算子不动点定理。作为应用,我们研究了无限区间上Banach空间中非线性积－微分方程初值问题解的存在性。     

Some Convergence Results for a Class of Nonlinear Phase-Field Evolution Equations

Two heat diffusion problems in the framework of the parabolic phase-field model are presented. The first problem is related to a single isotropic fluid and the other describes the heat transmission between two different substances in contact. Some known existence and uniqueness results are briefly recalled. Then, an asymptotic analysis of both situations is carried out as the kinetic equation collapses to a temperature-phase relation of Stefan type, in the first case in the whole material, and in the second in only one of the substances. In both cases, a convergence result for the solutions is proved. The second problem shows some more mathematical difficulties that are due to the presence of nontrivial terms on the common boundary. In order to control the latter, some tools are used from the Γ-convergence theory for convex functionals.     

Optimal Control Problems for a Class of Semilinear Multisolution Elliptic Equations

We study the optimal control problem for a class of elliptic problems that may possess multiple solutions. We obtain necessary conditions for optimal control by constructing a related parabolic problem and using known results for the parabolic problem.     

Type I operators and the approximation of singular two-point boundary value problems

A class of self adjoint operators associated with second order singular ordinary differential expressions, arises naturally when the problem is weakly formulated and integration by parts is performed. We call this class Type I operators. It turns out that this class can be successfully used to tackle numerical approximations of singular two-point boundary value problems. They can also be approximated by regular differential operators in a straightforward manner without having to bring the delicate structure of singular differential operators to the forefront of the investigation.     

Existence of Solutions for Nonlinear Implicit Differential Equations: An Equilibrium Problem Approach

In this article, we study the existence of solutions for nonlinear implicit differential equations associated to a time-dependent pseudomonotone (respectively, quasimonotone) operator by using a new approach based on the theory of equilibrium \hboxproblems. More precisely, we first establish some existence results of solutions for mixed equilibrium problems where the \hboxbifunctions are, respectively, maximal monotone and \hboxpseudomonotone (quasimonotone) in the topological sense. Then, we write the nonlinear implicit differential equations in the form of a mixed equilibrium problem. By using the existence results for mixed equilibrium problems, we establish the existence of solutions of nonlinear implicit differential equations. This new approach provides some new and nice results which improve and unify most of the recent results obtained in this direction.     

New classes of second order difference equations solvable by factorization method

Under some assumptions we find a general solution of the factorization problem for a family of second order difference equations.