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Journal ArticleDOI

Monotone iterative technique for second order delayed periodic problem in Banach spaces

01 Nov 2015-Applied Mathematics and Computation (Elsevier)-Vol. 270, pp 654-664
TL;DR: This paper builds a new maximum principle for the ω-periodic solutions of the corresponding linear equation with delay and studies the existence of the minimal and maximal periodic solutions for abstract delayed equation by combining perturbation method and monotone iterative technique of the lower and upper solutions.
About: This article is published in Applied Mathematics and Computation.The article was published on 2015-11-01. It has received 12 citations till now. The article focuses on the topics: Maximum principle & Banach space.
Citations
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Journal ArticleDOI

640 citations

01 Jan 2004
TL;DR: In this article, the problem of finding positive periodic solutions for a class of nonlinear second order ODEs was discussed and some existence and multiplicity results of positive periodic solution were derived.
Abstract: This paper discusses the problem of positive periodic solutions for a class of nonlinear second order ordinary differential equations.By utilizing a fixed point theorem on cone,some existence and multiplicity results of positive periodic solutions are derived.Our results improve theorems in the literature.

14 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian operator and obtained the existence and uniqueness of mild solutions under some quasimonotone conditions.
Abstract: This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of mild solutions for the abstract time-space evolution equation with delay under some quasimonotone conditions are obtained. Finally, the abstract results are applied to the time-space fractional delayed diffusion equation with fractional Laplacian operator, which improve and generalize the recent results of this issue.

7 citations

Journal ArticleDOI
TL;DR: In this paper, the existence of extremal solutions for a type of fractional compartment models is investigated. But the authors only consider the extremal solution of a single compartment model.
Abstract: In this paper, we consider the existence of extremal solutions for a type of fractional compartment models. By use of a new comparison result, some new sufficient conditions for the existence of solutions are established by combining the monotone iterative technique and the methods of lower and upper solutions. Finally, an example is presented to illustrate the validity of our main results.

1 citations

References
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Book
14 Oct 1993
TL;DR: The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977 and attempts to maintain the spirit of that book and have retained approximately one-third of the material intact.
Abstract: The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977. The authors have attempted to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a completely new presentation of linear systems (Chapter 6-9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global attractors was thoroughly revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (Chapters 1,2,3,9,10). Chapter 12 is also entirely new and contains a guide to active topics of research. In the sections on supplementary remarks, the authors have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive.

6,844 citations


"Monotone iterative technique for se..." refers background in this paper

  • ...The theory of differential equations with delays is an important branch of differential equation theory, which has extensive physical, biological, economical, engineering background and realistic mathematical model, and hence has been emerging as an important area of investigation in the last few decades, and the numerous properties of their solutions have been studied, see [6,7] and references therein....

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Book
01 Oct 1984
TL;DR: A survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis can be found in this article, with extensive commentary, many examples, and interesting, challenging exercises.
Abstract: This graduate-level text offers a survey of the main ideas, concepts, and methods that constitute nonlinear functional analysis. It features extensive commentary, many examples, and interesting, challenging exercises. Topics include degree mappings for infinite dimensional spaces, the inverse function theory, the implicit function theory, Newton's methods, and many other subjects. 1985 edition.

4,910 citations


"Monotone iterative technique for se..." refers background in this paper

  • ...For the details of the definition and properties of the measure of noncompactness, see [1,3,5]....

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Journal ArticleDOI

2,725 citations


"Monotone iterative technique for se..." refers background in this paper

  • ...For the details of the definition and properties of the measure of noncompactness, see [1,3,5]....

    [...]

Journal ArticleDOI

640 citations