2019
Том 71
№ 5

# 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

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