一类三独立变量六重和差分不等式中未知函数的估计

研究了一类具有三独立变量的六重非线性和差分不等式,和号外含非常数因子,和项外包含了非常数项.利用差分算子的性质、求和技巧、变量替换技巧和积分中值定理等手段,给出了和差分不等式中未知函数的上界估计,推广了已有结果.最后举例说明所得结果可以用来研究三独立变量差分方程解的定性性质.

Estimation of unknown functions in a calss of sixfold sum-difference inequalities in three independent variables

Sum-difference inequalities are the important tools to study existence, boundedness, uniqueness, continuous dependence of solutions on parameters and other qualitative properties of solutions of the difference equations. This paper studies a class of sixfold sum-difference inequalities in three independent variables, which include a nonconstant factor outside summarizing symbols and a nonconstant term outside summation term. The upper bounds of the unknown function in the sum-difference inequality is estimated explicitly using properties of difference operators, summing techniques, the techniques of change of variable, the method of amplification, the integral mean value theorem, and other analysis techniques, which generalized some known results. Finally an example is given to illustrate the results which is able to be used to study the qualitative properties of solutions of the difference equations with three independent variables.