Some remarks on linear functional differential inequalities of hyperbolic type - Šremr, J. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
It is proved that for the validity of a theorem on differential inequalities for the hyperbolic equation ^2u(t, x)t x = l(u)(t,x)+q(t,x) with a nonincreasing linear operator l: C([a, b]× [c,d];R)→L([a, b]× [c,d];R), it is necessary that the operator indicated be an (a, c)-Volterra operator.