Báo Cáo Báo cáo hóa học SOLVABILITY CONDITIONS FOR SOME DIFFERENCE OPERATORS

SOLVABILITY CONDITIONS FOR SOME DIFFERENCE OPERATORS N. C. APREUTESEI AND V. A. VOLPERT Received 24 June 2004

Infinite-dimensional difference operators are studied. Under the assumption that the coefficients of the operator have limits at infinity, limiting operators and associated polynomials are introduced. Under some specific conditions on the polynomials, the operator is Fredholm and has the zero index. Solvability conditions are obtained and the exponential behavior of solutions of the homogeneous equation at infinity is proved.

1. Introduction

Infinite-dimensional difference operators may not satisfy the Fredholm property, and the Fredholm-type solvability conditions are not necessarily applicable to them. In other words, we do not know how to solve linear algebraic systems with infinite matrices. Various properties of linear and nonlinear infinite discrete systems are studied in [1, 2, 3, 4, 5, 6, 7, 8]. The goal of this paper is to establish the normal solvability for