On the solvability of a complete second-order differential equation in Banach space - Gershtein, L. M. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
For the complete second-order differential equation with unbounded operator coefficients u’’ + A(t)u’ + B(i)u = f, u(0) = u_o, u’(0)=u_1 the Cauchy problem is studied. By using the "coinmutant method", we construct the coercive solution of this problem is in the Holder space in the case where the operator В has the same "strength" as the operator А^2.