A NEW NONLINEAR SUM-DIFFERENCE INEQUALITY AND ITS APPLICATION

Difference inequalities are important tools in the study of existence,uniqueness, boundedness,stability and other qualitative properties of solutions of difference equations. Many mathematicians not only study various generalizations of Gronwall inequality and their applications,but also study various difference inequalities.In this paper,we establish a new nonlinear sum-difference inequality,and the estimation of unknown function in the inequality is given by using a analytic technique.Furthermore,the result is used to boundary value problems of retarded difference equations and to get the estimation of solutions of the difference equation.