A family of two-point boundary value problems for loaded differential equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2021), pp. 13-24.

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A family of two-point boundary value problems for loaded differential equations is considered on rectangular domain. By introducing new additional functions considered problem is reduced to equivalent family problems for differential equations with parameters. Sufficient conditions of the existence unique solution to family of two-point boundary value problems for loaded differential equations are established in the terms of input data.
Keywords: family two-point boundary value problems, loaded differential equations, differential equations with parameters, solvability.
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A. T. Assanova; A. Zholamankyzy. A family of two-point boundary value problems for loaded differential equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2021), pp. 13-24. http://geodesic.mathdoc.fr/item/IVM_2021_9_a1/

[1] Babenko K.I., Teoreticheskie osnovy i konstruirovanie chislennykh algoritmov zadach matematicheskoi fiziki, Nauka, M., 1979

[2] Nakhushev A.M., “Ob odnom priblizhennom metode resheniya kraevykh zadach dlya differentsialnykh uravnenii i ego prilozheniya k dinamike pochvennoi vlagi i gruntovykh vod”, Differents. uravneniya, 18:1 (1982), 72–81 | Zbl

[3] Nakhushev A.M., Uravneniya matematicheskoi biologii, Vyssh. shk., M., 1995

[4] Boichuk A. A., Samoilenko A. M., Generalized inverse operators and Fredholm boundary-value problems, VSP, Utrecht–Boston, 2004 | Zbl

[5] Brunner H., Collocation methods for Volterra integral and related functional equations, Cambridge Univ. Press, London, 2004 | Zbl

[6] Abdullaev V. M., Aida-zade K. R., “O chislennom reshenii nagruzhennykh sistem obyknovennykh differentsialnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 44:9 (2004), 1585–1595

[7] Dzhenaliev M. T., Ramazanov M. I., Nagruzhennye uravneniya kak vozmuscheniya differentsialnykh uravnenii, GYLYM, Almaty, 2010

[8] Nakhushev A. M., Nagruzhennye uravneniya i ikh primenenie, Nauka, M., 2012

[9] Asanova A. T., Imanchiev A. E., Kadirbaeva Zh. M., “O chislennom reshenii sistem obyknovennykh nagruzhennykh differentsialnykh uravnenii s mnogotochechnymi usloviyami”, Zh. vychisl. matem. i matem. fiz., 58:4 (2018), 520–529 | Zbl

[10] Assanova A. T., Kadirbayeva Zh.M., “On the numerical algorithms of parametrization method for solving a two-point boundary-value problem for impulsive systems of loaded differential equations”, Comp. and Appl. Math., 37:4 (2018), 4966–4976 | DOI | Zbl

[11] Nakhushev A. M., “Kraevye zadachi dlya nagruzhennykh integro-differentsialnykh uravnenii giperbolicheskogo tipa i nekotorye ikh prilozheniya k prognozu pochvennoi vlagi”, Differents. uravneniya, 15:1 (1979), 96–105 | Zbl

[12] Pulkina L. S., “Nelokalnaya zadacha dlya nagruzhennogo giperbolicheskogo uravneniya”, Tr. MIAN, 236, 2002, 298–303 | Zbl

[13] Nakhushev A. M., Zadachi so smescheniem dlya uravnenii v chastnykh proizvodnykh, Nauka, M., 2006

[14] Nakhusheva V. A., Differentsialnye uravneniya matematicheskikh modelei nelokalnykh protsessov, Nauka, M., 2006

[15] Assanova A. T., Imanchiev A. E., “On the solvability of a nonlocal boundary value problem for a loaded hyperbolic equations with multi-point conditions”, Bull. Karaganda Univer.-Math., 81:1 (2016), 15–25

[16] Assanova A. T., Kadirbayeva Zh.M., Bakirova E. A., “About of an unique solvability of a nonlocal boundary value problem for the loaded systems of hyperbolic equations with impulse effects”, Ukr. Math. J., 69:8 (2018), 1175–1195 | DOI | Zbl

[17] Assanova A. T., Kadirbayeva Zh.M., “Periodic problem for an impulsive system of the loaded hyperbolic equations”, Electronic J. Diff. Equat., 2018:72 (2018), 1–8

[18] Asanova A. T., Imanchiev A. E., Kadirbaeva Zh. M., “O razreshimosti nelokalnoi zadachi dlya sistemy differentsialnykh uravnenii sobolevskogo tipa s mnogotochechnym usloviem”, Izv. vuzov. Matem., 2019, no. 12, 3–15 | Zbl

[19] Dikinov Kh. Zh., Kerefov A. A., Nakhushev A. M., “Ob odnoi kraevoi zadache dlya nagruzhennogo uravneniya teploprovodnosti”, Differents. uravneniya, 12:1 (1976), 77–179

[20] Nakhushev A. M., Borisov V. N., “Kraevye zadachi dlya nagruzhennykh parabolicheskikh uravnenii i ikh prilozheniya k prognozu urovnya gruntovykh vod”, Differents. uravneniya, 13:1 (1977), 105–110 | Zbl

[21] Khudalov M. Z., “Nelokalnaya kraevaya zadacha dlya nagruzhennogo uravneniya parabolicheskogo tipa”, Vladikavkazsk. matem. zhurn., 4:4 (2002), 59–64 | Zbl

[22] Kozhanov A. I., “Nelineinye nagruzhennye uravneniya i obratnye zadachi”, Zh. vychisl. matem. i matem. fiz., 44:4 (2004), 694–716 | Zbl

[23] Alikhanov A. A., Berezgov A. M., Shkhanukov–Lafishev M. Kh., “Kraevye zadachi dlya nekotorykh klassov nagruzhennykh differentsialnykh uravnenii i raznostnye metody ikh chislennoi realizatsii”, Zh. vychisl. matem. i matem. fiz., 48:9 (2008), 1619–1628

[24] Abdullaev V. M., Aida-zade K. R., “Konechnoraznostnye metody resheniya nagruzhennykh parabolicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 56:1 (2016), 99–112 | Zbl

[25] Dzhumabaev D. S., “Priznaki odnoznachnoi razreshimosti lineinoi kraevoi zadachi dlya obyknovennogo differentsialnogo uravneniya”, Zh. vychisl. matem. i matem. fiz., 29:1 (1989), 50–66 | Zbl

[26] Dzhumabaev D. S., “Singulyarnye kraevye zadachi i ikh approksimatsiya dlya nelineinykh obyknovennykh differentsialnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 32:1 (1992), 13–29

[27] Dzhumabaev D. S., Temesheva S. M., “Metod parametrizatsii resheniya nelineinykh dvukhtochechnykh kraevykh zadach”, Zh. vychisl. matem. i matem. fiz., 47:1 (2007), 39–63 | Zbl

[28] Dzhumabaev D. S., Bakirova E. A., “Priznaki korrektnoi razreshimosti lineinoi dvukhtochechnoi kraevoi zadachi dlya sistem integro-differentsialnykh uravnenii”, Differents. uravneniya, 46:4 (2010), 550–564 | Zbl

[29] Asanova A. T., Dzhumabaev D. S., “Odnoznachnaya razreshimost kraevoi zadachi s dannymi na kharakteristikakh dlya sistem giperbolicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 42:11 (2002), 1673–1685 | Zbl

[30] Asanova A. T., Dzhumabaev D. S., “Odnoznachnaya razreshimost nelokalnykh kraevykh zadach dlya sistem giperbolicheskikh uravnenii”, Differents. uravneniya, 39:10 (2003), 1343–1354 | Zbl

[31] Asanova A. T., Dzhumabaev D. S., “Well-posedness of nonlocal boundary value problems with integral condition for the system of hyperbolic equations”, J. of Math. Anal. and Appl., 402:1 (2013), 167–178 | DOI | Zbl

[32] Dzhumabaev D. S., Asanova A. T., “Priznaki korrektnoi razreshimosti lineinoi nelokalnoi kraevoi zadachi dlya sistem giperbolicheskikh uravnenii”, Dopovidi NAN Ukraini, 2010, no. 4, 7–11 | Zbl