一类含下界函数的非线性差分不等式的比较定理

COMPARISON THEOREM FOR A CLASS OF NONLINEAR DIFFERENCE INEQUALITIES CONTAINING INFIMUM FUNCTIONS

对一类含下界函数的非线性差分不等式证明了一个比较定理，这类不等式是Ｎａｋａｏ不等式的逆转不等式，因而所得结果可用来估计某些发展方程解的渐近衰减阶数的下界。而ＮａＫａｏ原结果只能用于解的增长上界估计。

A comparison theorem is proved for a class of nonlinear difference inqualities.containinginfunum of the unknown functions.Each inequality from this class is an inverse differenceinequality of Nakao's inequality.Hence the comparison theorem proved is useful in the estima-tion of the infimum of so solutions to some nonlinear evolutions equations.However,the originalresults of Nakao can be used only when the supremum of solutions is considered.A numberof application examples are also given.