In this paper we study the asymptotic behavior of the solution of the new class of the nonlinear rational Difference Equations. Namely, we consider the stability, boundedness, and periodicity of the solution. Moreover we give the periodic character of solutions of these equations, which is not familiar. We do not know a similar feature for other class of the nonlinear rational Difference Equati...

The eigenfrequencies associated to a damped wave equation are known to belong to a band parallel to the real axis. Under the assumption of periodicity of the geodesic flow we study the asymptotic distribution of the eigenfrequencies in the band. We show that the set of eigenfrequencies exhibits a cluster structure determined by the Morse index of the closed geodesics and the damping coefficient...

This paper is concerned with a problem in the theory of elasticity for a thin composite plate. The principal terms are constructed for the asymptotics of the solution, with only local periodicity of the elastic moduli of the material and the shape of the plate assumed. The asymptotic expression is justified with the help of a weighted anisotropic Korn’s inequality, which is proved by means of t...

In this paper, we study the existence of monotone positive solutions which converge to the equilibrium of a nonlinear difference equation. Recently, there has been a lot of interest in studying such solutions and the existence of some specific solutions see 1–20 . In 8 , Karakostas and Stević studied the boundedness, global attractivity, and oscillatory and asymptotic periodicity of the nonnega...

This paper studies the boundedness, global asymptotic stability, and periodicity of positive solutions of the equation xn f xn−2 /g xn−1 , n ∈ N0, where f, g ∈ C 0,∞ , 0,∞ . It is shown that if f and g are nondecreasing, then for every solution of the equation the subsequences {x2n} and {x2n−1} are eventually monotone. For the case when f x α βx and g satisfies the conditions g 0 1, g is nondec...