Mixed Monotone Iterative Technique for Abstract Impulsive Evolution Equations in Banach Spaces
نویسندگان
چکیده
منابع مشابه
Mixed Monotone Iterative Technique for Abstract Impulsive Evolution Equations in Banach Spaces
Impulsive differential equations are a basic tool for studying evolution processes of real life phenomena that are subjected to sudden changes at certain instants. In view of multiple applications of the impulsive differential equations, it is necessary to develop the methods for their solvability. Unfortunately, a comparatively small class of impulsive differential equations can be solved anal...
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We use a monotone iterative method in the presence of lower and upper solutions to discuss the existence and uniqueness of mild solutions for the initial value problem u′(t) + Au(t) = f(t, u(t), Tu(t)), t ∈ J, t 6= tk, ∆u|t=tk = Ik(u(tk)), k = 1, 2, . . . , m, u(0) = x0, where A : D(A) ⊂ E → E is a closed linear operator and −A generates a strongly continuous semigroup T (t)(t ≥ 0) in E. Under ...
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and Applied Analysis 3 The purpose of this paper is to improve and extend the above mentioned results. We will delete the Lipschitz condition 1.5 for impulsive function Ik and the restriction condition 1.6 and improve condition 1.4 for nonlinear term f . Our main results are as follows. Theorem 1.1. Let E be an ordered Banach space, whose positive cone P is normal, A : D A ⊂ E → E be a closed l...
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This paper deals with the existence of L-quasi-solutions for impulsive periodic boundary value problems in an ordered Banach space E. Under a new concept of upper and lower solutions, a new monotone iterative technique on periodic boundary value problems of impulsive differential equations has been established. Our result improves and extends some relevant results in abstract differential equat...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2010
ISSN: 1029-242X
DOI: 10.1155/2010/293410