Abstract
We investigate the higher order nonlinear discrete Volterra equations. We study solutions with prescribed asymptotic behavior. For example, we establish sufficient conditions for the existence of asymptotically polynomial, asymptotically periodic or asymptotically symmetric solutions. On the other hand, we are dealing with the problem of approximation of solutions. Among others, we present conditions under which any bounded solution is asymptotically periodic. Using our techniques, based on the iterated remainder operator, we can control the degree of approximation. In this paper we choose a positive non-increasing sequence u and use o(un) as a measure of approximation.
Highlights
We denote by N the set of positive integers and by R the set of real numbers
In this paper we investigate asymptotic behavior of solutions to Equation (1) which is a discrete analog of Equation (2)
Studies on solutions with prescribed asymptotic behavior are usually based on the application of the Schauder or Darboux type theorems
Summary
We denote by N the set of positive integers and by R the set of real numbers. Assume τ is an integer, m ∈ N, 2021, 13, 918. https://doi.org/. The second problem is the approximation of a given solution of Equation (1). Studies on solutions with prescribed asymptotic behavior are usually based on the application of the Schauder or Darboux type theorems. In this case, conditions of the continuity type are superimposed on the function f. The asymptotic properties of solutions to the Volterra equations of the monotonic type have not been studied. They are the main results of the paper.
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