Том 71
№ 4

All Issues

Petrovskii Ya. B.

Articles: 2
Article (Ukrainian)

The solvability of a boundary-value periodic problem

Khoma G. P., Petrovskii Ya. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 302–308

In the space of functions B a 3+ ={g(x, t)=−g(−x, t)=g(x+2π, t)=−g(x, t+T3/2)=g(x, −t)}, we establish that if the condition aT 3 (2s−1)=4πk, (4πk, a (2s−1))=1, k ∈ ℤ, s ∈ ℕ, is satisfied, then the linear problem u u −a 2 u xx =g(x, t), u(0, t)=u(π, t)=0, u(x, t+T 3 )=u(x, t), ℝ2, is always consistent. To prove this statement, we construct an exact solution in the form of an integral operator.

Brief Communications (Ukrainian)

Periodic solutions of Quasilinear Hyperbolic integro-differential equations of second order

Petrovskii Ya. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1572-1575

We study a periodic boundary-value problem for a quasilinear integro-differential equation with the d’Alembert operator on the left-hand side and a nonlinear integral operator on the right-hand side. We establish conditions under which the uniqueness theorems are true.