On the solvability of a complete second-order differential equation in Banach space

The paper deals with the Cauchy problem for a complete second-order differential equation with unbounded operator coefficientsu+A(t)u+B(t)u=f, u(0)=u0, u(0)=u ₁ . By using the commutant method, we construct a coercive solution of this problem in Holder space in the case where the operatorB is as strong as the operator A².Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1449–1454, October, 1993.