Sufficient conditions are given for the relation limt→∞y(t)=0
to hold, where y(t) is a continuous nonnegative function on [0,1)
satisfying some nonlinear inequalities. The results are used for a study of
large time behavior of the solutions to nonlinear evolution equations. Example
of application is given for a solution to some evolution equation with a
nonlinear partial differential operator.Comment: 16 page