Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces
Keyword(s):
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 spaceE:u′(t)+Au(t)=f(t,u(t),Gu(t)),t∈[0,a],t≠tk,Δu|t=tk=Ik(u(tk)),0<t1<t2<⋯<tm<a,u(0)=u0, whereA:D(A)⊂E→Eis a closed linear operator, andf:[0,a]×E×E→Eis a nonlinear mapping. Under wide monotone conditions and measure of noncompactness conditions of nonlinearityf, some existence and uniqueness results are obtained by using a monotone iterative technique in the presence of lower and upper solutions.
2008 ◽
Vol 221
(1)
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pp. 158-164
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2010 ◽
Vol 2010
(1)
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pp. 293410
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2020 ◽
Vol 21
(2)
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pp. 205-218