scholarly journals Monotone iterative technique for S-asymptotically periodic problem of fractional evolution equation with finite delay in ordered Banach space

2021 ◽  
pp. 521-546
Author(s):  
Qiang Li ◽  
Mei Wei
Keyword(s):  
Banach Space ◽  
Evolution Equation ◽  
Periodic Problem ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Ordered Banach Space ◽  
Monotone Iterative ◽  
Fractional Evolution Equation ◽  
Finite Delay ◽  
Asymptotically Periodic

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 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 Periodic problem for non-instantaneous impulsive partial differential equations

2021 ◽  
Vol 7 (3) ◽  
pp. 3345-3359
Author(s):  
Huanhuan Zhang ◽  
◽  
Jia Mu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mild Solutions ◽  
Periodic Problem ◽  
Lower Solution ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Partial Differential ◽  
Monotone Iterative ◽  
Impulsive Equation

<abstract><p>We obtain a new maximum principle of the periodic solutions when the corresponding impulsive equation is linear. If the nonlinear is quasi-monotonicity, we study the existence of the minimal and maximal periodic mild solutions for impulsive partial differential equations by using the perturbation method, the monotone iterative technique and the method of upper and lower solution. We give an example in last part to illustrate the main theorem.</p></abstract>

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 Monotone iterative technique for Caratheodory theory of nonlinear functional random integral equations

2002 ◽  
Vol 33 (4) ◽  
pp. 341-352 ◽  
Author(s):  
B. C. Dhage
Keyword(s):  
Banach Space ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Random Fixed Point ◽  
Nonlinear Functional ◽  
Monotone Iterative ◽  
Monotonicity Conditions ◽  
Random Integral

In this paper some random fixed point theorems for the mappings on an ordered Banach space are proved. As applications, the existence of the extremal solutions of some nonlinear functional random integral equations is obtained under certain monotonicity conditions.

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