Applications to Infinite Systems of Differential Equations

Józef Banaś () and Mohammad Mursaleen ()
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Józef Banaś: Rzeszów University of Technology, Department of Mathematics
Mohammad Mursaleen: Aligarh Muslim University, Department of Mathematics

Chapter Chapter 7 in Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, 2014, pp 219-262 from Springer

Abstract: Abstract In this chapter we apply the machinery developed previously to the theory of ordinary differential equations in Banach spaces. In particular, we show that several infinite systems of differential equations in some Banach sequence spaces can be treated from the view point of the theory of differential equations in Banach spaces. Moreover, using some specific features of sequence spaces we are able to formulate several results concerning the solvability of infinite systems of differential equations in numerous sequence spaces and to characterize solutions of those systems. We illustrate results presented in this chapter by many concrete examples.

Keywords: Ordinary differential equation; Peano theorem; Kamke comparison function; Measure of noncompactness; Kernel set; Infinite system of differential equations; Semilinear infinite system of differential equations; Perturbed diagonal infinite system of differential equations; Perturbed semilinear upper diagonal infinite system of differential equations; Asymptotic coordinable stability (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1886-9_7

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DOI: 10.1007/978-81-322-1886-9_7

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