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| SOME GENERALIZATION OF GRONWALL-BIHARI INTEGRAL INEQUALITIES AND THEIR APPLICATIONS |
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Citation： |
Kong Qingkai,Zhang Binggen.SOME GENERALIZATION OF GRONWALL-BIHARI INTEGRAL INEQUALITIES AND THEIR APPLICATIONS[J].Chinese Annals of Mathematics B,1989,10(3):371~385 |
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Net amount： 811 |
Authors： |
Kong Qingkai; Zhang Binggen |
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| Abstract： |
The interest of this paper lies in the estimates of solutions of the three kinds of Gronwan-Bihari integral inequalities:
(I) $\[y(x) \le f(x) + \sum\limits_{i = 1}^n {{g_i}(x)\int_0^x {{h_i}(s)y(s)ds,} } \]$
(II)$\[y(x) \le f(x) + g(x)\psi (\int_0^x {h(s)w(y(s))ds} )\]$
(III)$\[y(x) \le f(x) + \sum\limits_{i = 1}^n {{g_i}(x)\int_0^x {{h_i}(s)y(s)ds} + {g_{n + 1}}(x)\psi (\int_0^s {{h_{n + 1}}(s)w(y(t))ds} ).} \]$
The results include some modificstions and generalizations of the results of D. Willett U. D. Dhongade and Zhang Binggen. Furthermore, applying the conclusion on the above
inequalities to a Volterra integral equation and a differential equation, the authors obtain some new better results. |
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