一类含有未知导函数的积分不等式中未知函数的界

The bound of an unknown function of a class of integral inequalities with unknown derivative function

研究了一类非线性积分不等式,其中被积函数中含有未知函数的方幂及其导函数的幂次,积分号外包含了常数项和非常数项。通过放大、变量代换、求导、积分等分析方法,给出了积分不等式中未知函数的界。

A class of nonlinear integral inequalities is established,which includes the power of unknown function and its derivative function in integral function,and a nonconstant factor and a constant factor are included outside integral sign.The bound of the unknown function in the integral inequality is estimated explicitly using the techniques of variable substitution,amplification,derivation and integration.