Solvability of infinite systems of second order differential equations in \(c_0\) and \(\ell_1\) by Meir-Keeler condensing operators. (English) Zbl 1385.47021
In this paper, the authors consider infinite systems of second order differential equations in Banach sequence spaces \(c_0\) and \(\ell_1\) and prove existence results for those problems. The main tool used in the proofs is the fixed point theorem for Meir-Keeler condensing operators (here, the condensity is considered in view of the Hausdorff measure of noncompactness)
The main results are illustrated by suitable examples.
The main results are illustrated by suitable examples.
Reviewer: Dariusz Bugajewski (Poznań)
MSC:
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
| 47N20 | Applications of operator theory to differential and integral equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
Keywords:
Darbo’s fixed point theorem; infinite system of differential equations; measure of noncompactness; Meir-Keeler condensing operatorsCitations:
Zbl 0194.44904References:
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