Perturbation technique for a class of nonlinear implicit semilinear impulsive integro-differential equations of mixed type with noncompactness measure

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• 作者：Heng-you Lan (1) (2)
  Yi-shun Cui (3)
  
  1. Institute of Nonlinear Science and Engineering Computing ; Sichuan University of Science & Engineering ; Zigong ; Sichuan ; 643000 ; P.R. China
  2. Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things ; Zigong ; Sichuan ; 643000 ; P.R. China
  3. College of Materials and Chemical Engineering ; Sichuan University of Sciences & Engineering ; Zigong ; Sichuan ; 643000 ; P.R. China
  
• 关键词：nonlinear first ; order implicit semilinear impulsive integro ; differential equation ; monotone iterative technique ; monotone condition and noncompactness measure condition ; lower and upper solution ; existence and uniqueness
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,189 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

By using the Arzela-Ascoli theorem, the Bellman inequality, and a monotone perturbation iterative technique in the presence of lower and upper solutions, we discuss the existence of mild solutions for a class of nonlinear first-order implicit semilinear impulsive integro-differential equations in Banach spaces. Under wide monotone conditions and the noncompactness measure conditions, we also obtain the existence of extremal solutions and a unique mild solution between lower and upper solutions.