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.     

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.     

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.     

On the Global Character of the Difference Equation X n + 1 =

We investigate the global stability, the periodic character, and the boundedness nature of solutions of the difference equation x n +1 = f + n x n m (2 k +1) + i x n m 2 l A + x n m 2 l , n =0,1,… where k and l are non-negative integers, the parameters f , n , i , A are non-negative real numbers with f + n + i >0, and the initial conditions are non-negative real numbers. We show that the solutions exhibit a trichotomy character depending upon the parameters n , i and A .     

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.     

Exact Closed Form Solution for Two Coupled Inhomogeneous First Order Difference Equations with Variable Coefficients

We present an exact closed form solution for two coupled, homogeneous as well as inhomogeneous, first order difference equations with variable coefficients. The solution is obtained by using the graph theoretic, discrete path formalism. The central parameters in the solution are the crossing index and the crossing number. The transition from an enumerative graph theoretic solution to a closed form combinatorial solution is made possible by an isomorphism in-between paths on the signal flow graph, and n -tuplets of binary numbers.     

Difference Equations∶ Detecting Oscillations via Higher Order Characteristic Equations

In these notes we introduce an alternative procedure to detect the presence of a wide range of oscillatory solutions-the exponential oscillatory ones-in both continuous-time and discrete linear difference equations. The technique is addressed to the scalar case of the linear two-delay difference equation, but it can be extended to other types of evolution equations including the nonlinear ones, in higher dimensions. In particular, we give an illustration of its applicability to the case of a simple two dimensional difference equation. Oscillatory solutions are presented in their closed formulae.