### Homogeneous Problem with two-point in time Conditions for Some Equations of Mathematical Physics

#### Abstract

We study the problem for homogeneous partial differential equations of two variables

of the second order with respect to the time variable in which there given homogeneous two-point

conditions, and finite order with respect to another (spatial) variable. We propose a method of

construction nontrivial solutions of the problem when the characteristic determinant of the problem

is nontrivial and the set of its zeroes is not empty. We applied this method to the construction of

non-zero solutions of homogeneous two-point problems for some equations of mathematical physics.

#### Keywords

#### Full Text:

PDF#### References

V. M. Borok, Uniqueness classes for the solution of a boundary problem in an infinite

layer., Dokl. Akad. Nauk SSSR, 183(5), 1968, 995–998.

B. Yo. Ptashnyk, Ill-posed boundary value problems for partial differential equations,

Nauk. Dumka, 1984.

B. Yo. Ptashnyk, V. S. Il’kiv, I. Ya. Kmit, V. M. Polishchuk, Nonlocal boundary value

problems for partial differential equations, Nauk. dumka, 2002.

P. I. Kalenyuk, Z. M. Nytrebych, Generalized scheme of separation of variables.

Differential-symbol method, Publishing House of Lviv Polytechnic National University,

P. I. Kalenyuk, Ya. Ye. Baranetskyi, Z. N. Nytrebych, Generalized method of separation

of variables, Nauk. Dumka, 1983.

V. S. Il’kiv, Z. M. Nytrebych, On solutions of the homogeneous Dirihlet problem in

the time strip for the partial differential equation of the second order with respect to

time variable, Visn. Lviv. Univ., Ser. mekh-mat., 78, 2013, 65–77.

P. I. Kalenyuk, I. V. Kogut, Z. M. Nytrebych, Differential-symbol method of solving

the problem with nonlocal boundary condition for partial differential equation, Mat.

Met. Fiz.-Meh. Polya, 45(2), 2002, 7–15.

Z. M. Nytrebych, A boundary-value problem in an unbounded strip, J. Math. Sci.,

(6), 1996, 1388–1392.

P. Ya. Pukach, Qualitative research methods of mathematical model of nonlinear vibrations

of conveyor, J. Math. Sci., 198(1), 2014, 31–36.

A. N. Tihonov, A. B. Vasil’eva, A. G. Sveshnikov, Differential equations, Nauka, 1980.

Z. M. Nytrebych, O. M. Malanchuk, The homogeneous problem with boundary conditions

on the border of the strip for partial differential equation of second order in

time, Nauk. Visn. Uzhorod. Univ, 2 (27), 2015, 98–108.

### Refbacks

- There are currently no refbacks.