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

Advances in Difference Equations

Yi-shun Cui¹  Heng-you Lan² 

[1] Engineering, Zigong, P.R. China;Institute of Nonlinear Science and Engineering Computing, Sichuan University of Science &Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Zigong, 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;   

DOI  :  10.1186/s13662-014-0329-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY