一类新的脉冲积分不等式及其应用
A Class of New Impulsive Integral Inequality and Its Application
摘要: 本文建立了一类新的非连续函数积分和不等式，其不等式左端为未知函数的非线性因子，右端和项中也为未知函数的非线性因子。我们给出了未知函数的界的估计。最后，我们用求得的结果给出了脉冲微分方程解的估计。
Abstract: In this paper, we establish a class of new integro-sum inequality for discontinuous function, and the left hand of the inequality is a nonlinear factor of unknown function, and the sum-term of the right hand of the inequality for the unknown function is also a nonlinear factor. We obtain the estimation of bound of the unknown function. Finally, we apply our result to present estimation of the solution of impulsive differential equation.
文章引用：李自尊, 黄勇. 一类新的脉冲积分不等式及其应用[J]. 理论数学, 2013, 3(1): 41-45. http://dx.doi.org/10.12677/PM.2013.31007

参考文献

[1] W. Zhang, S. Deng. Projected Gronwall-Bellman’s inequality for integrable functions. Mathematical and Computer Modelling, 2001, 34(3-4): 394-402.
[2] S. K. Choi, S. F. Deng, N. J. Koo and W. Zhang. Nonlinear integral inequalities of Bihari-Type without class H. Mathematical Inequalities & Application, 2005, 8(4): 643-654.
[3] W. S. Wang. A generalized retarded Gronwall-like inequality in two variables and applications to BVP. Applied Mathematics and Computation, 2007, 191(1): 144-154.
[4] W. S. Wang. Estimation on certain nonlinear discrete inequality and applications to boundary value problem. Advances in Difference Equations, 2009, 2009: Article ID: 708587.
[5] R. P. Agarwal, S. Deng and W. Zhang. Generalization of a retarded Gronwall-like inequality and its applications. Applied Mathematics and Computation, 2005, 165(3): 599-612.
[6] W. S. Cheung. Some new nonlinear inequalities and applications to boundary value problems. Nonlinear Analysis, 2006, 64: 2112-2128.
[7] R. P. Agarwal, Y. H. Kim and S. K. Sen. New retarded integral inequalities with applications. Journal of Inequalities and Applications, 2008, 2008: Article ID: 908784.
[8] C. J. Chen, W. S. Cheung and D. Zhao. Gronwall-Bellman-Type integral inequalities and applications to BVPs. Journal of Inequalities and Applications, 2009, 2009: Article ID: 258569.
[9] S. D. Borysenko. About asymptotical stability on linear approximation of the systems with impulse influence. Ukrainian Mathematical Journal, 1983, 35(2): 144-150.
[10] A. M. Samoilenko, N. Perestyuk. Differential equations with impulse effect. Kyiv: Visha Shkola, 1987.
[11] S. D. Borysenko. About one integral inequality for piece-wise continuous functions. Proceedings of X. International Kravchuk Conference, Kyiv, 2004: 323.
[12] G. Iovane. Some new integral inequalities of Bellman-Bihari type with delay for discontinuous functions. Nonlinear Analysis, 2007, 66: 498-508.
[13] A. Gallo, A. M. Piccirillo. About new analogies of Gronwall-Bellman-Bihari type inequalities for discontinuous functions and estimated solutions for impulsive differential systems. Nonlinear Analysis, 2007, 67: 1550-1559.
[14] Y. A. Mitropolskiy, G. Iovane and S. D. Borysenko. About a generalization of Bellman-Bihari type inequalities for discontinuous functions and their applitions. Nonlinear Analysis: Theory, Methods & Applications, 2007, 66(10): 2140-2165.
[15] A. Gallo, A. M. Piccirillo. On some generalizations Bellman-Bihari result for integro-functional inequalities for discontinuous functions and their applications. Boundary Value Problems, 2009, 2009: Article ID: 808124.
[16] A. Gallo, A. M. Piccirillo. About some new generalizations of Bellman-Bihari results for integro-functional inequalities with discontinuous functions and applications. Nonlinear Anal, 2009, 71(12): 2276-2287.

为你推荐