Existence criteria for positive solutions of a nonlinear difference inequality
Tom 73 / 2000
Annales Polonici Mathematici 73 (2000), 197-220 DOI: 10.4064/ap-73-3-197-220
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.