New comparison results for impulsive integro-differential equations and applications

By J. J. Nieto, Rosana Rodríguez-López. 2007

164 citations recorded by the source corpus.

We prove some new maximum principles for ordinary integro-differential equations. This allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first-order impulsive integro-differential equation.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/142cbcfa8ca5df3daae7f6aa2b08062d98450f26

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yong Ren
2. Xinzhu Meng
3. Zuomao Yan
4. Hongwu Zhang

In Control and Systems Engineering

1. Yong Ren
2. Zuomao Yan
3. Hongwu Zhang

In Numerical Analysis

1. Yong Ren
2. Xinzhu Meng

Citations in the corpus

• A Stage-Structured Predator-Prey SI Model with Disease in the Prey and Impulsive Effects (2013, background): “In recent years, impulsive systems are found in many research areas of applied sciences [7,10,15,19,21].”
• Asymptotic stability of impulsive stochastic partial differential equations with infinite delays (2009, unknown): “The theory of impulsive differential equations has been studied extensively (see [16,17] and references therein).”
• Existence Results for Impulsive Neutral Stochastic Functional Integro-Differential Equations with Infinite Delays (2010, background): “In addition, impulsive effects exist in many evolution processes in which states are changed abruptly at certain moments of time, involved in such fields as medicine and biology, economics, bioengineering, chemical technology etc. (see [ 11 , 15] and reference therein).”