Nevanlinna Theory For Jackson Difference Operators And Q-difference Equations

The main purpose of this thesis is to establish the Nevanlinna theory for Jackson difference operator(?).By using these theory,we investigate the entire solutions of linear q-difference equations(?),and estimate the logarithmic order of some q-functions.The first chapter is the introduction,which first introduces the research background and original purpose of Nevanlinna theory,then introduces the current research status of Jackson difference operators.In the second chapter is the preliminary knowledge,which states the classical Nevanlinna theory,Nevanlinna theory of(?)and(?)difference operator,Askey-wilson difference operator and Wilson difference operator.In the third chapter,we give our results on Jackson difference operator's Nevanlinna theory,such as logarithmic derivative lemma,second fundamental theorem,Clunie lemma,Mohon'ko lemma,defect relation,Picard theorem.In chapter 4,we study some results of the solution of Jackson's difference equation,such as Jackson kernel,two linearly independent solutions of second-order Jackson q-difference equation,and entire solutions of linear and nonlinear Jackson q-difference equation.Finally,we give some examples to verify these results.The fifth chapter is the summary and prospect.On the one hand,We summarized this article.On the other hand,some unresolved problems are put forward.