ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE

By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.     

GLOBAL EXISTENCE OF STRONG SOLUTIONS OF NAVIER-STOKES EQUATIONS WITH NON-NEWTONIAN POTENTIAL FOR ONE-DIMENSIONAL ISENTROPIC COMPRESSIBLE FLUIDS

The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS

In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given.     

ON THE EXISTENCE AND UNIQUENESS OF CLASSICAL GLOBAL SOLUTION TO A TYPE OF B0USSINESQ EQUATIONS

The existence and uniqueness of classical global solutions to a type of Boussinesq equations withinitial and boundary values are studied in this paper. The existence of such solutions is proved bymeans of compactness theorem and Schauders fixed point theorem, and its uniqueness by the so calledenergy method.     

THE NONLOCAL INITIAL PROBLEMS OF A SEMILINEAR EVOLUTION EQUATION

The purpose of this paper is to investigate the existence of solutions to a nonlocal Cauchy problem for an evolution equation. The methods used here include the semigroup methods in proper spaces and Schauder's theorem. And the results are applied to a system of nonlinear partial differential equations with nonlinear boundary conditions.     

ALMOST PERIODIC SOLUTIONS TO SOME NONLINEAR DELAY DIFFERENTIAL EQUATION

The existence of an almost periodic solutions to a nonlinear delay diffierential equation is considered in this paper. A set of sufficient conditions for the existence and uniqueness of almost periodic solutions to some delay diffierential equations is obtained.     

Pseudo Almost Automorphic Solutions for Non-autonomous Stochastic Differential Equations With Exponential Dichotomy

In this paper, we consider the existence and uniqueness of the solutions which are pseudo almost automorphic in distribution for a class of non-autonomous stochastic differential equations in a Hilbert space. In conclusion, we use the Banach contraction mapping principle and exponential dichotomy property to obtain our main results.     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH DELAY

Using a fixed point method, in this paper we discuss the existence and uniqueness of positive solutions to a class system of nonlinear fractional differential equations with delay and obtain some new results.     

THE EXISTENCE OF THE SOLUTIONS FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS

The author obtains the existence of the local and global solution for a class of semilinear evolution equations in a Hilbert spcae, and uses the results to prove the existence of the solution for semilinear parabolic partial differential equations in R~n.     

STRUCTURE OF POSITIVE SOLUTIONS OF A CLASS OF QUASILINEAR ORDINARY DIFFERENTIAL EQUATIONS

The existence and uniqueness of positive solutions for a class of quasilinearordinary differential equations with a large parameter are obtained. It is shownthat the flat core of positive solutions can exist. So some results of [1-3] aresharpened.     

The Existence and Uniqueness of Solutions of a Class of Evolution Equations

In this paper, a class of evolution equations which have special boundary conditions is discussed. The spectrum properties of an operator which is associated with this class of equations arc provided, and the existence and uniqueness of solutions of this class of equations is proved by the theory of pertu rbation of C_0-semigroups. In the last part of this paper, a condition which ensures the solutions to be non-negative is given. Some results of the time-independent population systems in [1-5] are our examples.     

The solvability of some chemotaxis systems

In this paper, we study the local existence and uniqueness of classical solutions to a wide class of systems of chemotaxis equations. These systems are essentially quasi-linear strongly coupled partial differential equations. We also study the maximal interval of existence in time of solutions. The results are illustrated in application to a number of partial differential equation models arising in biology.     

一类脉冲微分系统的有界变差解

在比文[6]更弱的条件下讨论了固定时刻脉冲微分系统与Kurzweil广义常微分方程的关系，并建立了这类脉冲微分系统有界变差解的局部存在性和唯一性定理．     

On the optimal control of systems governed by quasilinear integro-partial differential equations of parabolic type

Recently, M. N. O?uztöreli presented certain results on the existence and uniqueness of solutions of systems governed by a linear integro-partial differential equation of parabolic type with delayed arguments. Since his results admit only smooth coefficients, they could not be used directly in the study of the optimal control problems with bounded measurable control variables appearing in the coefficients of the system equations. In this paper, we consider a class of systems described by second-order quasilinear parabolic integro-partial differential equations with all but the second-order coefficients assumed bounded measurable. Our principal results are: Theorem 3.5, which establishes the existence and uniqueness of solutions of this class of systems (with controls in the coefficients), and Theorem 4.4, which gives a necessary condition for optimality for the corresponding controlled system.     

非混合单调二元算子方程(组)解的存在唯一性

利用锥理论及Banach压缩映射原理,在不要求上、下解条件及算子紧性与连续性的条件下,建立了一类满足更一般序关系条件的非混合单调二元算子方程组(?)解的存在唯一性定理,以及非单调二元算子方程T(x,x)=x和非单调一元算子方程Lx=x解的存在唯一性定理,推广了最近相关文献的研究结果.     

Teoremi di esistenza e di unicitá per le soluzioni deboli dei problemi al contorno per una classe di sistemi parabolici di equazioni del secondo ordine

In this paper we give some existence and uniqueness theorems for weak solutions of boundary value problems for a particular class of parabolic systems of linear partial differential equations of the second order with real coefficients. In particular some uniqueness theorems for equations with complex coefficients are deduced from the previous results.     

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

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＴＨＥＳＹＳＴＥＭＳＯＦＭＩＸＥＤＭＯＮＯＴＯＮＥＯＰＥＲＡＴＯＲＥＱＵＡＴＩＯＮＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＨＥＮＰＥＩＬＯＮＧ...     

动态规划中提出的一类泛函方程组公共解和重合解的存在性定理

本文讨论了动态规划中提出的一类更一般的泛函方程组公共解和重合解的存在性问题.本文的结果不仅包含引文[6,7]中相应结果为特例,而且也对引文[2～5]在讨论动态规划的原理和模型时所提出的一类新型的泛函方程给出解的存在性条件.     

u0 - 凹算子的不动点定理及其应用

该文利用锥的性质和单调迭代技巧讨论了u₀ - 凹算子正不动点的存在唯一性,所得结论改进并推广了已有的相关结果. 作为应用, 该文研究了一类Hammerstein积分方程正解的存在唯一性.