Abstract and Applied Analysis

Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces

He Yang

Full-text: Open access

Abstract

This paper deals with the existence and uniqueness of mild solutions for the initial value problems of abstract impulsive evolution equations in an ordered Banach space E : u ( t ) + A u ( t ) = f ( t , u ( t ) , G u ( t ) ) , t [ 0 , a ] , t t k , Δ u | t = t k = I k ( u ( t k ) ) , 0 < t 1 < t 2 < < t m < a , u ( 0 ) = u 0 , where A : D ( A ) E E is a closed linear operator, and f : [ 0 , a ] × E × E E is a nonlinear mapping. Under wide monotone conditions and measure of noncompactness conditions of nonlinearity f , some existence and uniqueness results are obtained by using a monotone iterative technique in the presence of lower and upper solutions.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 481648, 11 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620750

Digital Object Identifier
doi:10.1155/2010/481648

Mathematical Reviews number (MathSciNet)
MR2672193

Zentralblatt MATH identifier
1235.34211

Citation

Yang, He. Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces. Abstr. Appl. Anal. 2010 (2010), Article ID 481648, 11 pages. doi:10.1155/2010/481648. https://projecteuclid.org/euclid.aaa/1288620750


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