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ArticleOriginal scientific text

Title

Existence criteria for positive solutions of a nonlinear difference inequality

Authors 1, 2

Affiliations

  1. Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, R.O.C.
  2. Department of Mathematics, Datong Advanced College, Datong, Shanxi 037008, P.R. China

Abstract

This paper is concerned with a class of nonlinear difference inequalities which include many different classes of difference inequalities and equations as special cases. By means of a Riccati type transformation, necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained. Various type of comparison theorems are also derived as applications, which extends many theorems in the literature.

Keywords

ENG
Sturm type comparison theorem, limit comparison theorem, nth order linear difference equation, eventually positive solution, eventually positive nonincreasing solution, neutral difference equation, nonlinear delay difference inequality

Bibliography

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Annales Polonici Mathematici
2000/73/3
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Pages:
197-220
Main language of publication
English
Received
1998-07-08
Accepted
1998-12-15
Published
2000
Exact and natural sciences