The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem

• Autorzy: Nytrebych, Zinovii , Malanchuk, Oksana
• Języki publikacji: EN

Abstrakty

EN

The solvability of the problem with local nonhomogeneous two-point in time conditions for a homogeneous PDE of the second order in time and infinite order in spatial variable in the case when the set of zeroes of the characteristic determinant is not empty and does not coincide with C is investigated. The existence of a solution of the problem in which the right-hand sides of the two-point conditions are quasi-polynomials is proved. We propose the differential-symbol method of constructing the solutions of the problem.

Słowa kluczowe

PL

warunki dwupunktowe; wyznacznik charakterystyczny; metoda różniczkowa; rozwiązania quasi-wielomianu

EN

two-point conditions; characteristic determinant of a problem; differential-symbol method; quasi-polynomial solutions

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 88--96
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Nytrebych, Zinovii

• Lviv Polytechnic National University, Lviv, Ukraine,

autor

Malanchuk, Oksana

• Danylo Halytsky Lviv National Medical University, Lviv, Ukraine,

Bibliografia

• [1] Vallee-Poussin Ch. J., Sur l’equation differentielle lineaire du second ordre. Determination d’une integrale par deux valeurs assignees Extension aux equations d’ordren, J. Math. Pures Appl. (9), 1929, 8, 125–144
• [2] Picone M., Sui valori eccezionali di un parametro do cui dipend un equazione differentiale lineare ordinaria del secondo ordine, Pisa, 1909
• [3] Tamarkin Ya. D., About the some general problem of the theory of ordinary differential equations and expansion of arbitrary functions in series, Pg., 1917
• [4] Ptashnyk B. Yo., Problem of Vallee-Poussin type for hyperbolic equations with constant coeflcients, DAN URSR, 1966, 10, 1254–1257
• [5] Kiguradze T., The Vallee-Poussin problem for higher order nonlinear hyperbolic equations, Comput. Math. Appl., 2010, 59(2), 994–1002
• [6] Ptashnyk B. Yo., Ill-posed boundary value problems for partial differential equations, Nauk. Dumka, Kyiv, 1984
• [7] Ptashnyk B. Yo., Il’kiv V. S., Kmit I. Ya., Polishchuk V. M., Nonlocal boundary value problems for partial differential equations, Nauk. dumka, Kyiv, 2002
• [8] Ptashnyk B. Yo., Symotyuk M. M., Multipoint problem for nonisotropic partial differential equations with constant coeflcients, Ukr. Math. Journ., 2003, 55(2), 293–310
• [9] Borok V. M., Uniqueness classes for the solution of a boundary problem in an infinite layer, Dokl. Akad. Nauk SSSR, 1968,183(5), 995–998
• [10] Borok V. M., Perelman M. A., Unique solution classes for a multipoint boundary value problem in an infinite layer, Izv. Vyss. Ucebn. Zaved. Matematika, 1973, 8, 29–34
• [11] Vilents’ I. L., The classes of uniqueness of the solution of a general boundary-value problem in a layer for systems of linear partial differential equations, Dop. Akad. Nauk URSR, 1974, 3, 195–197
• [12] Fardigola L. V., Well-posed problems in a layer with differential operators in boundary conditions, Ukr. Math. J., 1992, 44(8),983–989
• [13] Fardigola L. V., Nonlocal two-point boundary-value problems in a layer with differential operators in the boundary condition, Ukr. Math. J., 1995, 47(8), 1283–1289
• [14] Hayman W. K., Shanidze Z. G., Polynomial solutions of partial differential equations, Methods Appl. Anal., 1999, 6(1), 97–108
• [15] Hile G. N., Stanoyevitch A., Heat polynomial analogous for equations with higher order time derivatives, J. Math. Anal. Appl., 2004, 295, 595–610
• [16] Pedersen P., A basis for polynomial solutions for systems of linear constant coeflcient PDE’s, Adv. Math., 1996, 117, 157–163
• [17] Kalenyuk P., Nytrebych Z., Generalized scheme of separation of variables, Differential-symbol method, Publishing House of Lviv Polytechnic National University, Lviv, 2002
• [18] Kalenyuk P. I., Kohut I. V., Nytrebych Z. M., Problem with integral condition for partial differential equation of the first order with respect to time, J. Math. Sci., 2012, 181(3), 293–304
• [19] Nitrebich Z. M., A boundary-value problem in an unbounded strip, J. Math. Sci., 1996, 79(6), 1388–1392
• [20] Nitrebich Z. M., An operator method of solving the Cauchy problem for a homogeneous system of partial differential equations, J. Math. Sci., 1996, 81(6), 3034–3038
• [21] Nytrebych Z., Malanchuk O., The differential-symbol method of solving the two-point problem with respect to time for apartial differential equation, J. Math. Sci., 2017, 224(4), 541–554
• [22] Kempf A., Jackson D. M., Morales A. H., New Dirac delta function based methods with applications to perturbative expansions in quantum, J. Phys. Math. Theor., 2014, 47(41)
• [23] Kempf A., Jackson D. M., Morales A. H., How to (parth) integrate by differentiating, J. Phys.: Conf. Ser., 2015, 626
• [24] Malanchuk O., Nytrebych Z., Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables, Open Math., 2017, 15, 101–110
• [25] Nytrebych Z., Malanchuk O., Il’kiv V., Pukach P., Homogeneous problem with two-point in time conditions for some equations of mathematical physics, Azerb. J. Math., 2017, 7(2), 180–196
• [26] Nytrebych Z., Il’kiv V., Pukach P., Malanchuk O., On nontrivial solutions of homogeneous Dirichlet problem for partial differential equations in a layer, Kragujevac J. Math., 2018, 42(2), 193–207
• [27] Nytrebych Z., Malanchuk O., Il’kiv V., Pukach P., On the solvability of two-point in time problem for PDE, Italian J. Pure Appl. Math., 2017, 38, 715–726

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).

Identyfikatory

DOI

10.1515/dema-2019-0010