Abstract and Applied Analysis

Compactness Conditions in the Theory of Nonlinear Differential and Integral Equations


Publishing date
22 Feb 2013
Status
Published
Submission deadline
05 Oct 2012

Lead Editor

1Department of Mathematics, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959 Rzeszów, Poland

2Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India

3Departamento de Matematicas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain


Compactness Conditions in the Theory of Nonlinear Differential and Integral Equations

Description

It is well known that the classical Schauder fixed point principle plays an important role in proving the existence of solutions both of differential and integral equations. Obviously the basic tool exploited in that fixed point principle is the compactness of operators associated with investigated equations. Apart from the aforementioned Schauder fixed point principle, there exist several other theorems and methods used in the theory of differential and integral equations which are based on compactness conditions. For example, Krasnosel'skii fixed point theorem and its numerous generalizations as well as Arino-Gautier-Penot fixed point theorem for weakly sequentially continuous operators utilize the methods and reasonings associated with compactness conditions. It is worthwhile mentioning that the technique of measures of noncompactness, which is widely used in the last decades, is realized essentially via compactness conditions. Recently, there appeared several research papers treating various aspects of operator theory with help of the use of compactness or weak compactness conditions in connection with applications to the theory of differential and integral equations.

We invite authors to supply original research as well as review articles concerning numerous topics in which compactness conditions play an important role. We are especially interested in paper showing the applicability of compactness conditions in the theory of differential and integral equations. The papers indicating new directions of the investigations with the use of compactness conditions are also warmly invited. Potential topics include, but are not limited to:

  • Fixed point theorems based on compactness and weak compactness argumentations
  • Applications of compactness conditions in proving existence theorems for differential equations
  • Nonlinear integral equations of various type via the compactness conditions
  • Finite and infinite systems of differential and integral equations with the use of compactness conditions
  • The technique of measures of noncompactness and its application to the theory of differential and integral equations

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/aaa/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/ according to the following timetable:


Articles

  • Special Issue
  • - Volume 2013
  • - Article ID 616481
  • - Editorial

Compactness Conditions in the Theory of Nonlinear Differential and Integral Equations

Józef Banaś | Mohammad Mursaleen | ... | Kishin Sadarangani
  • Special Issue
  • - Volume 2013
  • - Article ID 819315
  • - Review Article

Compactness Conditions in the Study of Functional, Differential, and Integral Equations

Józef Banaś | Kishin Sadarangani
  • Special Issue
  • - Volume 2012
  • - Article ID 647103
  • - Research Article

Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions

Carlos Lizama | Juan C. Pozo
  • Special Issue
  • - Volume 2012
  • - Article ID 929870
  • - Research Article

On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays

Qiang Li | Yongxiang Li
  • Special Issue
  • - Volume 2012
  • - Article ID 932019
  • - Research Article

Solvability of Nonlinear Integral Equations of Volterra Type

Zeqing Liu | Sunhong Lee | Shin Min Kang
  • Special Issue
  • - Volume 2012
  • - Article ID 172963
  • - Research Article

Existence of Solutions for Fractional Integro-Differential Equation with Multipoint Boundary Value Problem in Banach Spaces

Yulin Zhao | Li Huang | ... | Xianyang Zhu
  • Special Issue
  • - Volume 2012
  • - Article ID 412948
  • - Research Article

Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations

Hassan Eltayeb | Adem Kılıçman
  • Special Issue
  • - Volume 2012
  • - Article ID 863483
  • - Review Article

Infinite System of Differential Equations in Some Spaces

M. Mursaleen | Abdullah Alotaibi
  • Special Issue
  • - Volume 2012
  • - Article ID 387629
  • - Research Article

Some Existence Results for Impulsive Nonlinear Fractional Differential Equations with Closed Boundary Conditions

Hilmi Ergören | Adem Kiliçman
  • Special Issue
  • - Volume 2012
  • - Article ID 239695
  • - Research Article

Some New Estimates for the Error of Simpson Integration Rule

Mohammad Masjed-Jamei | Marwan A. Kutbi | Nawab Hussain
Abstract and Applied Analysis
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