2019
Том 71
№ 11

All Issues

Gershtein L. M.

Articles: 3
Brief Communications (Russian)

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

Gershtein L. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1449–1454

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 $А^2$.

Brief Communications (Russian)

On a coupled system of abstract differential equations similar to the thermoelasticity equations

Gershtein L. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1162–1165

The study of a model system of differential equations arising from the dynamical problems of thermo elasticity is continued. The case of shifts of the general type is investigated. We employ the “commutant method” based on the properties of the operator $\Delta(A, B) = AB - BA$.

Article (Ukrainian)

A connected system of differential equations in a Banach space

Gershtein L. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 7. - pp. 898-905