On solutions of semilinear upper diagonal infinite systems of differential equations. (English) Zbl 1412.34188
Summary: The goal of the paper is to investigate the existence of solutions for semilinear upper diagonal infinite systems of differential equations. We will look for solutions of the mentioned infinite systems in a Banach tempered sequence space. In our considerations we utilize the technique associated with the Hausdorff measure of noncompactness and some existence results from the theory of ordinary differential equations in abstract Banach spaces.
MSC:
| 34G20 | Nonlinear differential equations in abstract spaces |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
infinite system of differential equation; Banach space; tempered sequence; semilinear upper diagonal infinite syatem of differential equations; measure of noncompactnessReferences:
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