L_n×L_2上几类特殊类型格蕴涵代数方程的解法

在格蕴涵代数中提出了加既约元、乘既约元,研究了一类重要的格蕴涵代数L_n×L_2中元素的不可约有限分解, 并将这一理论用于研究L_n×L_2上的几类格蕴涵代数方程,讨论了方程有解的充分必要条件,在此基础上给出了方程的具体解集.     

Generalized impedance boundary conditions for the maxwell equations as singular perturbations problems

In this paper the Maxwell equations in an exterior domain with generalaized impedance boundary conditions of Engquist-Nédélec are considered. The particular form of the assumed boundary conditions can be considered to be a singular perturbation of the Dirichlet boundary conditions. The convergence of the solution of the Maxwell equations with these generalized impedance boundary conditions to that of the corresponding Dirichlet problem is proven. The proof uses a new integral equations method combined with results dealing with singular perturbation problems of a class of pseudo-differential operators.     

Continuation Theory for Contractions on Spaces with Two Vector-Valued Metrics

We develop a continuation theory for contractive maps on spaces with two vector-valued metrics. Applications are presented for systems of operator equations in Banach spaces and, in particular, for systems of abstract Hammerstein integral equations. The use of vector-valued metrics makes it possible for each equation of a system to have its own Lipschitz property, while the use of two such metrics makes it possible for the Lipschitz condition to be expressed with respect to an incomplete metric.     

Periodic Solutions of Nonautonomous Discrete Predator-Prey System of Lotka-Volterra Type

A sufficiency criterion is established for the existence of positive periodic solutions of a nonautonomous discrete time predator-prey system of Lotka-Volterra type. Our approach is based on the coincidence degree and the related continuation theorem as well as some priori estimates.     

A Reproductive Property for a Class of Non-Newtonian Fluids

In this work we analyse a class of non-Newtonian reproductive fluid with a non-linear viscosity. The latter follows the power law or the Carreau's laws which is in common use for polymeric fluids. For a generalized data we introduce some special estimates and then obtain an existence result for the reproductive flow according to certain values of parameters appearing in the model.     

Theory of Differential Inequalities for Two-Point Boundary Value Problems and their Applications to Three-Point B.V.Ps Associated with n th Order Non-Linear System of Differential Equations

This paper presents a theory of differential inequalities for two-point boundary value problems (B.V.Ps) associated with the system of n th order non-linear differential equations. Using these inequalities as a tool we establish the existence and uniqueness of solutions to three-point B.V.Ps associated with the system of n th order non-linear differential equations by using the idea of matching solutions.     

More on the Difference Equation y n + 1 = ( p + y n −1 )/( qy n + y n −1 )

From previous studies of the equation in the title with positive parameters p and q and positive initial conditions we know that if q h 4 p + 1 then the equilibrium is a global attractor. We also know that if q > 4 p + 1 then every solution eventually enters and remains in the interval [ p / q , 1]. In this strip there exists a "unique" prime period two solution that is locally asymptotically stable. In this paper, we provide more insight as to the behavior of solutions of the equation in the title in the strip [ p / q , 1], where a one-dimensional stable manifold lives.     

Asymptotic Diagonalization and Normalization of Linear q -Difference Equations

Asymptotic diagonalizations of linear differential equations are studied by several authors. The problems for linear difference equations are investigated recently by Bodine and Sacker. In their work, the full spectrum condition plays essential role. Here we consider a related problem for q-difference equations, |q| < 1, which do not satisfy the full spectrum condition. Our tool is the Arnold normal form for matrix.     

Multiple Symmetric Solutions for Discrete Lidstone Boundary Value Problems

We offer criteria for the existence of single, double and multiple positive symmetric solutions for the boundary value problem ?^{2m y(k-m)= f(y(k), ?²y(k-1)….,?SUP>2i y(k-i),…,?2(m-1)} y(k-(m-1))), k∈{a+1,…,b+1} ?²ⁱ y(a+1-m)=?²ⁱ y(b+1+m-2i)=0, 0≤i≤m-1 where m ≥ 1 and (-1)^m f can either be positive or the condition can be relaxed.