Asymptotic Classification of Solutions of the Discrete Painlev\'E-1 Equation

TL;DR

This paper classifies solutions of the Discrete Painlevé-1 Equation based on their asymptotic behavior as the argument approaches infinity, providing existence theorems for these solutions.

Contribution

It offers a comprehensive classification of DP1 solutions and proves existence theorems, advancing understanding of their asymptotic properties.

Findings

Solutions are classified according to their asymptotic behavior.

Existence theorems for solutions with specific asymptotic properties are established.

The work enhances the theoretical understanding of DP1 solutions.

Abstract

The main subject of the paper is the so-called Discrete Painlev\'e-1 Equation (DP1). Solutions of the DP1 are classified under criterion of their behavior while argument tends to infinity. The appropriate theorems of existence are proved.