Asymptotic Behaviour of a Difference Equation with Complex-valued Coefficients
نویسندگان
چکیده
Abstract. The asymptotic behaviour for solutions of a difference equation ∆zn = f(n, zn), where the complex-valued function f(n, z) is in some meaning close to a holomorphic function h, and of a Riccati difference equation is studied using a Lyapunov function method. The paper is motivated by papers on the asymptotic behaviour of the solutions of differential equations with complex-valued right-hand sides.
منابع مشابه
Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case
The asymptotic behaviour for the solutions of a real two-dimensional system with a bounded nonconstant delay is studied under the assumption of instability. Our results improve and complement previous results by J. Kalas, where the sufficient conditions assuring the existence of bounded solutions or solutions tending to origin for t approaching infinity are given. The method of investigation is...
متن کاملAsymptotic distributions of Neumann problem for Sturm-Liouville equation
In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.
متن کاملAsymptotic Properties of an Unstable Two-dimensional Differential System with Delay
Abstract. The asymptotic behaviour of the solutions is studied for a real unstable twodimensional system x(t) = A(t)x(t) +B(t)x(t − r) + h(t, x(t), x(t − r)), where r > 0 is a constant delay. It is supposed that A, B and h are matrix functions and a vector function, respectively. Our results complement those of Kalas [Nonlinear Anal. 62(2) (2005), 207–224], where the conditions for the existenc...
متن کاملThe Asymptotic Form of Eigenvalues for a Class of Sturm-Liouville Problem with One Simple Turning Point
The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...
متن کاملTitle : ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR ( p ) PROCESSES
In this paper nearly unstable AR(p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behaviour of the least squares estimators of the coefficients. A convergence result is presented for the general complex-valued case. The limit distribution is given by the help of some continuous time AR processes. We appl...
متن کامل