Existence of solution for system of differential equations in $$c_{0}$$ and $$\ell _{1}$$ spaces

Autor: Ishfaq Ahmad Malik, Tanweer Jalal
Rok vydání: 2020
Předmět:
Zdroj: Afrika Matematika. 31:1129-1143
ISSN: 2190-7668
1012-9405
DOI: 10.1007/s13370-020-00785-2
Popis: The paper considers the system of second order differential equations of the form: $$\begin{aligned} \frac{\mathrm {d}^2v_{j}}{\mathrm {d}t^2}-v_{j}=f_{j}(t,v(t));~~~v_{j}(0)=v_{j}(T)=0 \end{aligned}$$ 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.
Databáze: OpenAIRE
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