On some continuous and discrete equations in Banach spaces on unbounded intervals. (Q1856047)

The authors study existence theorems for continuous problems of the form \[ y(t)= h(t)+ \int^t_0 K(s, t)f(s, y(s))\,ds,\quad t\in [0,\infty), \] and discrete problems of the form \[ y(i)= h(i)+ \sum^\infty_{j=0} G(i,j)f(j,y(j))\,ds,\quad i\in \{0,1,2,\dots\}, \] on the unbounded interval, where ``\(\int\)'' denotes the Pettis integral and \(f\) is weakly sequentially continuous.