Abstract
The paper considers the system of second order differential equations of the form:
where \(t\in [0,T]\), \(v(t)=\left( v_{j}(t)\right) _{j=1}^{\infty }\). The system is investigated in Banach spaces \(c_{0}\) and \(\ell _{1}\). Using the concept of measures of noncompactness, conditions for the existence of solution are found for the above system. The idea is supported with different examples.
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Malik, I.A., Jalal, T. Existence of solution for system of differential equations in \(c_{0}\) and \(\ell _{1}\) spaces. Afr. Mat. 31, 1129–1143 (2020). https://doi.org/10.1007/s13370-020-00785-2
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DOI: https://doi.org/10.1007/s13370-020-00785-2
Keywords
- Infinite system of second order differential equations
- Measures of noncompactness
- Darbo’s fixed point theorem