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

Józef Banaś | Zendy; Kishin Sadarangani | Zendy

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

Author(s) -

Józef Banaś,

Kishin Sadarangani

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/819315

Subject(s) - mathematics , compact space , fixed point theorem , banach space , mathematical analysis , ordinary differential equation , integral equation , differential equation , pure mathematics

We discuss some existence results for various types of functional, differential, and integral equations which can be obtained with the help of argumentations based on compactnessconditions. We restrict ourselves to some classical compactness conditions appearing in fixed point theorems due to Schauder, Krasnosel’skii-Burton, and Schaefer. We present also the technique associated with measures of noncompactness and we illustrate its applicability in proving the solvability of some functional integral equations. Apart from this, we discuss the application of the mentioned technique to the theory of ordinary differential equations in Banach spaces

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