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

He Yang

Abstract and Applied Analysis, 2010, vol. 2010, 1-11

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.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:481648

DOI: 10.1155/2010/481648

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