Integral Inequalities of Gronwall-Bellman-Bihari Type and Asymptotic Behavior of Certain Second Order Nonlinear Differential Equations
Integral Inequalities of Gronwall-Bellman-Bihari Type and Asymptotic Behavior of Certain Second Order Nonlinear Differential Equations
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DOI：
10.1016/0022-247x(85)90014-9
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发表时间：
1985-05
影响因子：
1.3
通讯作者：
F. Dannan
中科院分区：
文献类型：
--
作者：
F. Dannan
吸引人的Gronwall-Bellman不等式[IO]在研究微分方程解的稳定性和渐近性方面起着至关重要的作用（见[2，31]）。许多线性和非线性的推广已经出现在文献[6，181。Bihari不等式[4]是Gronwall-Bellman不等式最重要的推广。第二节得到了几个类似于Bellman-Bihari不等式的积分不等式。在第三节中，我们利用这些结果讨论了一类二阶非线性微分方程的渐近性态。
The attractive Gronwall-Bellman inequality [IO] plays a vital role in studying stability and asymptotic behavior of solutions of differential equations (see [2, 31). Many linear and nonlinear generalizations have appeared in the literature [6, 181. Bihari’s inequality [4] is the most important generalization of the Gronwall-Bellman inequality. Several integral inequalities similar to Bellman-Bihari’s inequality are obtained in Section 2. In Section 3 we use these results to discuss the asymptotic behavior of certain second order nonlinear differential equations.