探究解方程(组)的检验问题

解方程包含着＂解方程＂和＂检验＂两个步骤,并且缺一不可,无论解哪类方程（组）都是如此,本文就解方程（组）的检验问题进行一些研讨.

Iterative Solution for Systems of Binary Non-mixed Monotone Operator Equations

With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.

Blow-Up Rate for a Semilinear Parabolic System

This paper deals with the blow-up rate of positive solution for a semilinearparabolic system coupled in the equations and boundary condition. The upper and lower bounds ofblow-up rates are obtained.

Existence of Positive Solutions for a Class of Degenerate and Nondegenerate Stable Diffusion Models

This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.

Lienard Equation and Exact Solutions for Some Soliton-Producing NonlinearEquations

In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.

Existence of multi-bump solutions for coupled Schr dinger systems

The Schrodinger equation -△u＋λ2u=｜u｜2q-2u has a unique positive radial solution Uλ, which decays exponentially at infinity. Hence it is reasonable that the Schrolinger system -△u1＋u1=｜u1｜2q-1u1-εb（x）｜u2｜1｜u1｜q-1u1,-△u2＋u2=｜u2｜2q-2u2-εb（x）｜u1｜1｜u2｜q-1u2 has multiple-bump solutions which behave like Uλ in the neighborhood of some points. For u=（u1,u2）∈H1（R3）×H1（R3）, a nonlinear functional Iε（u）=I1（u1）＋I2（u2）-ε/q∫R3b（x）｜u1｜q｜u2｜qdx,is defined,where I1（u1）=1/2｜｜u1｜｜2-1/2q∫R3｜u1｜2qdx and I2（u2）=1/2｜｜u2｜｜2ω-1/2q∫R3｜u2｜2qdx. It is proved that the solutions of the system are the critical points of I,. Let Z be the smooth solution manifold of the unperturbed problem and TzZ is the tangent space. The critical point of I is rewritten as the form of z ＋ w, where w ∈ （TzZ）⊥. Using some properties of Iε, it is proved that there exists a critical point of I, close to the form which is a multi-bump solution.

Minor Self-conjugate and Skewpositive Semidefinite Solutions to a System of Matrix Equations over Skew Fields

Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.

Preconditioners for Incompressible Navier-Stokes Solvers

In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method.It is shown that block preconditioners form an excellent approach for the solution,however if the grids are not to fine preconditioning with a Saddle point ILU matrix(SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated.In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.

A Nonmonotone Trust Region Method for Solving Symmetric Nonlinear Equations

A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems.

Two-Soliton Solutions and Interactions for the Generalized Complex Coupled Kortweg-de Vries Equations

Kortweg-de Vries （KdV）-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV （GCCKdV） equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonie collisions are presented： （i） two solitons merge and separate from each other periodically; （ii） two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; （iii） two solitons are ftuctuant in the central region of the collision. Propagation features of solitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the a increasing. Amplitude of v increase with the a increasing and decrease with the β increasing.

Quenching for Degenerate Semilinear Reaction-diffusion Systems

In this paper, the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied. The regularization method and upper and lower solutions technique are employed to show the existence and continuation of a positive classical solution. The location of quenching points is found. The critical length is estimated by the eigenvalue method.

Application of Homotopy Analysis Method to Solve Relativistic Toda Lattice System

In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results show that homotopy analysis method is a powerful and easy-to-use analytic tool to solve systems of differential-difference equations.

Oscillations in Systems of Linear Neutral Differential Equations

Algebraic sufficient conditions are obtained for all nontrivial solutions of the linear system d d t[x(t)+cx(t-τ)]+A(t)x(t-σ(t))=0to be oscillatory.

A Mathod to Solve Systems of Fuzzy Linear Equations

Many systems of fuzzy linear equations do not have solutions when the solution concept is based on α cuts and interval arithmetic. In this paper,we establish the relations between the systems of fuzzy linear equations and the possibilistic linear programming problems and present an alternative method of solving the systems of fuzzy linear equations.

Existence and Regularity of Solution to a Thermally Coupled Nonstationary System

In this paper, a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied. Existence of a weak solution is first established through a result of Meyers＇ theorem and Schauder fixed point theorem, where the coupled functions σ（s）,k（s） are assumed to be bounded in the C（IR×（0, T））. If σ（s）,k（s） are Lipschitz continuous we prove that solution is unique under some restriction on integrability of solution. The regularity of the solution in dimension n ≤ 2 is then analyzed under the assumptions on σ（s） ∈w^1,∞（Ω×（0, T）） and the boundedness of σ＇（s） and σ″（s）.

Computation of Jordan Chains by Generalized Characteristic Matrices

In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.

The Smoothness of Weak Solutions to the System of Second Order Differential Equations with Non-negative Characteristics

In this paper,we will discuss smoothness of weak solutions for the system of second order differential equations eith non-negative characteristies.First of all,we establish boundary,and interior estimates and then we prove that solutions of regularization problem satisfy Lipschitz condition.

Existence and Life Span of Periodic Solutions for the First Order Quasilinear Hyperbolic Equations

In this paper the authors consider Cauchy problem of first order quasilinear hyperbolic and prove that existence of its periodic solutions and estimates of life span of solutions. This results reveals the relationship of dissipation and smoothness of periodic solutions.

A Novel Investigation on Using Strain in Barriers of 1.3 μm AlGaInAs-InP Uncooled Multiple Quantum Well Lasers

In this study we investigate strain effect in barriers of 1.3 μm AlCalnAs-InP uncooled multiple quantum well lasers. Single effective mass and Kohn-Luttinger Harniltonian equations have been solved to obtain quantum states and envelope wave functions in the structure. In the case of unstrained barriers, our simulations results have good agreement with a real device fabricated and presented in one of the references. Our main work is proposal of 0.2% compressive strain in the structure Barriers that causes significant reduction in Leakage current density and Auger current density characteristics in 85 ℃. 20% improvement in mode gain-current density characteristic is also obtained in 85 ℃.