一类新混合积分不等式及应用

A Kind of New Integral Inequalities and Its Applications

研究了如下混合积分不等式up(x,y)a(x,y)+b(x,y0)∫α(x)∫β∞y[c(s,t)u(s,t)+e(s,t)]dtds,up(x,y)a(x,y)0+∫α(x)b(s,y)[u(s,y)]pds+0∫α(x)∫β∞y[c(s,t)u(s,t)+e(s,t)]dtds及up(x,y)a(x,y)0+∫α(x)b(s,y)[u(s,y)]pds0+∫α(x)∫β∞yF(s,t,u(s,t))dtds,并给出了其具体的应用实例.

In this paper, the anthor mainly studies the retarded integral inequality p（x,y）≤a（x,y）＋b（x,y）f^a（x0∫^a（x）0∫^∞βy[c（s,t）u（s,t）＋e（s,t）]dtds,u^p（x,y）≤a（x,y）＋∫a（x）0b（s,y）[u（s,y）]）^pds＋∫α（x）0∫^∞βy[c（s,t）u（s,t）＋e（s,t）]dtds andu^p（x,y）≤a（x,y）＋∫^a（x）0b（s,y）[u（s,y）]^pds＋∫^α（x）0∫^∞βyF（s,t,u（s,t））dtds,the applications of these inequalities are also incloved.