A survey on measures of noncompactness with some applications in infinite systems of differential equations

2021 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Vladimir Rakočević
Keyword(s):  
Differential Equations ◽  
Measures Of Noncompactness ◽  
Infinite Systems ◽  
Systems Of Differential Equations

Application of Measure of Noncompactness to Infinite Systems of Differential Equations

2013 ◽  
Vol 56 (2) ◽  
pp. 388-394 ◽  
Author(s):  
M. Mursaleen
Keyword(s):  
Differential Equations ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Sequence Spaces ◽  
Measures Of Noncompactness ◽  
Infinite Systems ◽  
Systems Of Differential Equations ◽  
Banach Sequence Spaces ◽  
Banach Sequence

AbstractIn this paper we determine theHausdorff measure of noncompactness on the sequence space n(ϕ) ofW. L. C. Sargent. Further we apply the technique of measures of noncompactness to the theory of infinite systems of differential equations in the Banach sequence spaces n(ϕ) and m(ϕ). Our aim is to present some existence results for infinite systems of differential equations formulated with the help of measures of noncompactness.

scholarly journals Existence of solutions for infinite systems of differential equations by densifiability techniques

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3419-3428 ◽  
Author(s):  
Gonzalo García
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Main Tool ◽  
Measures Of Noncompactness ◽  
Infinite Systems ◽  
Novel Technique ◽  
Systems Of Differential Equations ◽  
General Conditions

A novel technique to state the existence of solutions for certain infinite systems of differential equations is proposed. Our main tool will be the so called degree of nondensifiability, which seems to work under more general conditions than the measures of noncompactness. In fact, in our main result, the required conditions proposed for the existence of solutions of such system are more general than others required in most of the results based on such measures.

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