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The equations considered in this paper are mixed-type functional equations (sometimes known as forward–backward differential equations) that take the form u′(t)=au(t)+bu(t−1)+cu(t+1),t∈I⊂R. We consider basic existence and uniqueness properties when I=[t1,t2] and we seek solutions u∈C[t1−1,t2+1] that satisfy u(t)=w1(t),t∈[t1−1,t1],u(t)=w2(t),t∈[t2,t2+1], for prescribed functions w1,w2 absolutely continuous,...
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