On functional differential equations in ordered Banach spaces (Q2784706)

The author deals with initial function problems for functional-differential equations of the type NEWLINE\[NEWLINEu'(t)- g(t,u)= f(t,u,u'(t)- g(t,u))\text{ a.e. in }[t_0,t_1],\;u(t)= B(t,u),\;t\in [t_0- r,t_0],NEWLINE\]NEWLINE in ordered Banach spaces. Under monotonicity and measurability assumptions on \(f\), \(g\) and \(B\), the author proves the existence of a least solution by means of a fixed-point theorem for monotone operators. Several examples illustrate the result.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00016].