Abstract
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.
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References
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1449–1454, October, 1993.
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Gershtein, L.M. On the solvability of a complete second-order differential equation in Banach space. Ukr Math J 45, 1629–1635 (1993). https://doi.org/10.1007/BF01571096
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DOI: https://doi.org/10.1007/BF01571096