On some continuous and discrete equations in Banach spaces on unbounded intervals

摘要

In this paper we study existence theorems for continuous and discrete problems of forms y(t)=h(t)+∫t0K(t,s)f(s,y(s))ds, t∈[0,∞) and y(i)=h(i)+∑j=0∞G(i,j)f(i,y(j)), i∈{0,1,2,…}, on the unbounded interval, where “∫” denote the Pettis integral and f is weakly–weakly sequentially continuous.