2019
Том 71
№ 11

All Issues

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

Gershtein L. M.

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Abstract

For the complete second-order differential equation with unbounded operator coefficients $u'' + A(t)u' + B(i)u = f, \quad u(0) = u_o, \quad u'(0)=u_1$ 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 $А^2$.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 10, pp 1629-1635.

Citation Example: Gershtein L. M. On the solvability of a complete second-order differential equation in Banach space // Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1449–1454.

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