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Application of measure of noncompactness to infinite systems of differential equations in \(\ell_p\) spaces. (English) Zbl 1447.34022
Using techniques associated with measures of noncompactness, the authors give conditions for the existence of solutions for the infinite system of second-order differential equations of the type \[ t\frac{d^2v_j}{dt^2}+\frac{dv_j}{dt}=f_j(t,v(t)),\;v_j(1)=v_j(T)=0, \] whith \(v(t)=(v_j(t))^{\infty}_{j=1}\) in the Banach sequence space \(\ell_p\), \(p\geq1\). The result is illustrated with a suitable example.

MSC:
34A35 Ordinary differential equations of infinite order
34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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