scholarly journals Monotone Iterative Technique for Fractional Evolution Equations in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Jia Mu
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Initial Value ◽  
Fractional Evolution Equations ◽  
Monotone Iterative ◽  
Noncompactness Measure

We investigate the initial value problem for a class of fractional evolution equations in a Banach space. Under some monotone conditions and noncompactness measure conditions of the nonlinearity, the well-known monotone iterative technique is then extended for fractional evolution equations which provides computable monotone sequences that converge to the extremal solutions in a sector generated by upper and lower solutions. An example to illustrate the applications of the main results is given.

scholarly journals Terminal value problems of impulsive integro-differential equations in Banach spaces

1997 ◽  
Vol 10 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Banach Spaces ◽  
Mixed Type ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
First Order ◽  
Monotone Iterative ◽  
Equations Of Mixed Type ◽  
Nonnegative Solutions

This paper uses cone theory and the monotone iterative technique to investigate the existence of minimal nonnegative solutions of terminal value problems for first order nonlinear impulsive integro-differential equations of mixed type in a Banach space.

scholarly journals Perturbation Results and Monotone Iterative Technique for Fractional Evolution Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
Jia Mu
Keyword(s):  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Ordered Banach Space ◽  
Fractional Evolution Equations ◽  
Existence And Uniqueness Results ◽  
Monotone Iterative ◽  
Fractional Evolution Equation ◽  
Uniqueness Results

We mainly study the fractional evolution equation in an ordered Banach space , , , . Using the monotone iterative technique based on lower and upper solutions, the existence and uniqueness results are obtained. The necessary perturbation results for accomplishing this approach are also developed.

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

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
He Yang
Keyword(s):  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Initial Value ◽  
Monotone Iterative ◽  
Uniqueness Results ◽  
Impulsive Evolution Equations

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.

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