Compactness Conditions in the Study of Functional, Differential, and Integral Equations
Keyword(s):
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 compactness conditions. 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.
2012 ◽
Vol 36
(6)
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pp. 659-673
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Fixed point theorems in the Fréchet space and functional integral equations on an unbounded interval
2012 ◽
Vol 218
(18)
◽
pp. 9066-9074
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2017 ◽
Vol 11
(2)
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pp. 340-357
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