On solutions of an infinite system of differentiam equations in classical Banach spaces
DOI:
https://doi.org/10.52934/wpz.2023.05Keywords:
difference equation, Banach space, measure of noncompactness, Infinite systems of differentia equations, Cauchy’s problemAbstract
The goal of the presented paper is the discussion of some theorems concerning the existence of solutions of Infinite systems of differentia equations in some Banach spaces. In the paper we consider two classical Banach sequence spaces, which frequently appear in considerations associated with Infinite systems of differentia equations.
Notice that infinite systems of differential equations occur often in several concrete applications to some topics of mechanics and modelling of the stochastic process of birth and death as well to the description of a lot of other problems.
The main tool used in the paper is the theory of measures on noncompactness and some theorems on the existence of solutions of differential equations in Banach spaces.
The results obtained in the paper are illustrated with the discussion of a few examples of infinite systems of differential equations.
References
Banaś, J., Goebel, K. (1980). Measures of Noncompactness in Banach Spaces, Lect. Notes in Pure and Appl. Math. 60, Marcel Dekker, New York.
Banaś, J., Lecko, M. (2001). Solvability of infinite systems of differential equations in Banach sequence spaces, J. Comput. Appl. Math. 137 363–375.
Banaś, J., Mursaleen, M. (2014). Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, New Delhi.
Deimling, K. (1977). Ordinary Differential Equations in Banach Spaces, Lect. Notes in Math. 596, Springer, Berlin.
Deimling, K. (1985). Nonlinear Functional Analysis, Springer, Berlin.
Fisz, M. (1980). Probability Theory and Mathematical Statistics, Krieger Publishing Company, New York, USA.
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