Positive Periodic Solutions For A Class Of First Order Difference Equations

The paper is concerned with the functional difference equationorIt consists of 4 chapters.In Chapter 1, we introduce the main work of the dissertation, the purpose of ourresearch and academic background and so on.In Chapter 2, by applying Leggett-Williams fixed point theorem to Eq.(1), whereA is a diagonal matrix, we show the explicit open intervals ofλsuch that the equa-tion has at least three nonnegative solutions.In Chapter 3, by applying Krasnosel'skii fixed point theorem, we obtain the exis-tence, multiplicity and nonexistence of positive T-periodic solutions to Eq.(2), whereA is a diagonal matrix. We show that the number of positive T-periodic solutions ofEq.(2) can be determined by the asymptotic behaviors of the quotient of f(xx )at zeroand infinity.In Chapter 4, as an application, a hematopoiesis model is given to illustrate ourresults.