Application of measure of noncompactness to infinite systems of differential equations in \(\ell_p\) spaces (Q777180)

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.