2019
Том 71
№ 11

# Khoma G. P.

Articles: 23
Article (Russian)

### Conditions of solvability of quasilinear periodic boundary-value problems for hyperbolic equations of the second order

Ukr. Mat. Zh. - 1998. - 50, № 6. - pp. 818–821

On the basis of properties of the Vejvoda-Shtedry operator, we obtain solvability conditions for the 2π-periodic problem $$u_{tt} - u_{xx} = F\left[ {u,u_t } \right], u\left( {0,t} \right) = u\left( {\pi ,t} \right) = 0, u\left( {x,t + 2\pi } \right) = u\left( {x,t} \right)$$ .

Article (Ukrainian)

### A periodic problem for the inhomogeneous equation of string oscillations

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 558–565

We study a periodic problem for the equation u tt−uxx=g(x, t), u(x, t+T)=u(x, t), u(x+ω, t)= =u(x, t), ℝ2 and establish conditions of the existence and uniqueness of the classical solution.

Article (Ukrainian)

### The solvability of a boundary-value periodic problem

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.

Article (Ukrainian)

### Existence of the Vejvoda-Shtedry spaces

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

We investigate the linear periodic problem u tt −u xx =F(x, t), u(x+2π, t)=u(x, t+T)=u(x, t), ∈ ℝ2, and establish conditions for the existence of its classical solution in spaces that are subspaces of the Vejvoda-Shtedry spaces.

Article (Ukrainian)

### On the periodic solutions of the second-order wave equations. V

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1115–1121

It is established that the linear problem $u_{tt} - a^2 u_{xx} = g(x, t),\quad u(0, t) = u(\pi, t),\quad u(x, t + T) = u(x, t)$ is always solvable in the space of functions $A = \{g:\; g(x, t) = g(x, t + T) = g(\pi - x, t) = -g(-x, t)\}$ provided that $aTq = (2p - 1)\pi, \quad (2p - 1, q) = 1$, where $p, q$ are integers. To prove this statement, an explicit solution is constructed in the form of an integral operator which is used to prove the existence of a solution to aperiodic boundary value problem for nonlinear second order wave equation. The results obtained can be employed in the study of solutions to nonlinear boundary value problems by asymptotic methods.

Article (Ukrainian)

### Periodic solutions of second-order wave equations. IV

Ukr. Mat. Zh. - 1988. - 40, № 6. - pp. 757–763

Article (Ukrainian)

### Periodic solutions of second-order wave equations. III

Ukr. Mat. Zh. - 1987. - 39, № 3. - pp. 347–353

Article (Ukrainian)

### Periodic solutions of second-order wave equations. II

Ukr. Mat. Zh. - 1986. - 38, № 6. - pp. 733-739

Article (Ukrainian)

### Periodic solutions of second-order wave equations. I.

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 593–600

Article (Ukrainian)

### Periodic solutions of second-order hyperbolic integrodifferential equations

Ukr. Mat. Zh. - 1986. - 38, № 4. - pp. 531–534

Article (Ukrainian)

### Analytic dependence of solutions of hyperbolic equations on a parameter

Ukr. Mat. Zh. - 1984. - 36, № 3. - pp. 396 - 398

Article (Ukrainian)

### Systems of van der pol equations in the resonance case

Ukr. Mat. Zh. - 1982. - 34, № 5. - pp. 655—656

Article (Ukrainian)

### The Banfi-Filatov theorem

Ukr. Mat. Zh. - 1982. - 34, № 2. - pp. 253-255

Article (Ukrainian)

### Discovery of periodic solutions of nonlinear first-order systems with distributed parameters

Ukr. Mat. Zh. - 1981. - 33, № 6. - pp. 779-786

Article (Ukrainian)

### Methods for averaging hyperbolic systems with rapid and slow variables mixed problem

Ukr. Mat. Zh. - 1979. - 31, № 4. - pp. 398–406

Article (Ukrainian)

### Averaging methods for hyperbolic systems with fast and slow variables Cauchy problem

Ukr. Mat. Zh. - 1979. - 31, № 2. - pp. 149–156

Article (Ukrainian)

### A method of averaging for hyperbolic integrodifferential systems with fast and slow variables

Ukr. Mat. Zh. - 1978. - 30, № 5. - pp. 696–701

Article (Ukrainian)

### Averaging in hyperbolic systems of standard form with retarded argument

Ukr. Mat. Zh. - 1978. - 30, № 1. - pp. 133–135

Article (Ukrainian)

### Averaging of first-order hyperbolic systems

Ukr. Mat. Zh. - 1976. - 28, № 4. - pp. 566–567

Article (Ukrainian)

### The teuncation of a countable system of partial differential equations

Ukr. Mat. Zh. - 1972. - 24, № 3. - pp. 417—420

Article (Ukrainian)

### On the averaging principle for hyperbolic equations along characteristics

Ukr. Mat. Zh. - 1970. - 22, № 5. - pp. 600—610

Article (Ukrainian)

### A theorem on averaging for hyperbolic systems of first order

Ukr. Mat. Zh. - 1970. - 22, № 5. - pp. 699—704

Article (Ukrainian)

### On the Bogolyubov-Mitropol'skii averaging principle for a class of second order hyperbolic equations

Ukr. Mat. Zh. - 1970. - 22, № 3. - pp. 388–393