一类和号内含有未知函数差分的和差分不等式中未知函数的估计

Estimation of Unknown Function of a Class of Sum-difference Inequalities with Difference of Unknown Function

研究了一类非线性和差分不等式,和号内不仅含有未知函数而且含有未知函数的差分,和项外包含了非常数项,利用各种分析手段,给出了和差分不等式中未知数的上界估计,推广了已有结果.最后举例说明所得结果可以用来研究和差分方程解的定性性质.

This paper studies a class of nonlinear sum-difference inequalities,which include an unknown function and its difference in summation term and a nonconstant factor outside summation term.The upper bounds of the unknown function in the sum-difference inequality is estimated explicitly using various means of analysis,which generalizes some known results.An example is given to illustrate that the results can be used to study the qualitative properties of solutions of the sum-difference equations.