一类含有奇异项的两个变量的复合Gronwall-Bellman型积分不等式及其应用
A Class of Composite Gronwall-Bellman Integral Inequality of Two Variables with Singular Terms and Its Application
DOI: 10.12677/aam.2025.1411455, PDF,    国家自然科学基金支持
作者: 李永盛*, 李自尊#, 莫小静：南宁师范大学数学与统计学院，广西 南宁
关键词: 复合积分不等式；偏微分方程；边值问题；Compound Integral Inequality； Partial Differential Equation； Boundary Value Problem
摘要: Gronwall-Bellman型积分不等式是研究微分方程解的定性性质的重要数学工具。本文研究了一类含有两个变量的复合Gronwall-Bellman型积分不等式，并利用得出的结果给出了偏微分方程中未知函数的上界估计。
Abstract: Gronwall-Bellman type integral inequality is an important mathematical tool to study the qualitative properties of the solutions of differential equations. In this paper, a class of complex Gronwall-Bellman type integral inequalities containing two variables is studied, and the upper bound estimates of unknown functions in partial differential equations are given by using the results obtained.
文章引用：李永盛, 李自尊, 莫小静. 一类含有奇异项的两个变量的复合Gronwall-Bellman型积分不等式及其应用[J]. 应用数学进展, 2025, 14(11): 1-12. https://doi.org/10.12677/aam.2025.1411455

参考文献

[1] Gronwall, T.H. (1919) Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential Equations. The Annals of Mathematics, 20, 292-296. [Google Scholar] [CrossRef] 
[2] Bellman, R. (1943) The Stability of Solutions of Linear Differential Equations. Duke Mathematical Journal, 10, 643-647. [Google Scholar] [CrossRef] 
[3] Pachpatte, B.G. (1973) A Note on Gronwall-Bellman Inequality. Journal of Mathematical Analysis and Applications, 44, 758-762. [Google Scholar] [CrossRef] 
[4] Pachpatte, D.B. (2006) Explicit Estimates on Integral Inequalities with Time Scale. Journal Inequalities in Pure and Applied Mathematics, 7, Article 143.
[5] Gu, J. and Meng, F. (2014) Some New Nonlinear Volterra-Fredholm Type Dynamic Integral Inequalities on Time Scales. Applied Mathematics and Computation, 245, 235-242. [Google Scholar] [CrossRef] 
[6] 王培, 陈心妍, 董琪翔. 含有两个变量的复合Gronwall-Bellman型积分不等式[J]. 大学数学, 2023, 39(1): 112-119.
[7] Henry, D. (1981) Geometric Theory of Semilinear Parabolic Equations. Springer-Verlag.
[8] Ye, H., Gao, J. and Ding, Y. (2007) A Generalized Gronwall Inequality and Its Application to a Fractional Differential Equation. Journal of Mathematical Analysis and Applications, 328, 1075-1081. [Google Scholar] [CrossRef] 

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