О разрешимости полного дифференциального уравнения второго порядка в банаховом пространстве

Abstract

For the complete second-order differential equation with unbounded operator coefficients u″+A(t)u′+B(i)u=f,u(0)=uo,u′(0)=u1 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 А2.