Glushak, A. V. On the unique solvability of nonlocal problems for abstract singular equations. (English. Russian original) Zbl 07885071 Math. Notes 115, No. 5, 706-718 (2024); translation from Mat. Zametki 115, No. 5, 690-704 (2024). MSC: 34G10 34B10 PDFBibTeX XMLCite \textit{A. V. Glushak}, Math. Notes 115, No. 5, 706--718 (2024; Zbl 07885071); translation from Mat. Zametki 115, No. 5, 690--704 (2024) Full Text: DOI
Glushak, A. V. On the solvability of initial and boundary value problems for abstract functional-differential Euler-Poisson-Darboux equations. (English) Zbl 07879101 Differ. Equ. 60, No. 3, 321-339 (2024). MSC: 47Dxx PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equ. 60, No. 3, 321--339 (2024; Zbl 07879101) Full Text: DOI
Arkhipov, V. P.; Glushak, A. V. First asymptotics of solutions of degenerate second-order differential equations. (English. Russian original) Zbl 1536.34014 Math. Notes 114, No. 6, 1107-1117 (2023); translation from Prikl. Mat. Fiz. 55, No. 3, 197-206 (2023). MSC: 34A30 34D05 PDFBibTeX XMLCite \textit{V. P. Arkhipov} and \textit{A. V. Glushak}, Math. Notes 114, No. 6, 1107--1117 (2023; Zbl 1536.34014); translation from Prikl. Mat. Fiz. 55, No. 3, 197--206 (2023) Full Text: DOI
Glushak, A. V. On the solvability of boundary value problems for an abstract singular equations on a finite interval. (English) Zbl 1533.34052 Lobachevskii J. Math. 44, No. 8, 3298-3308 (2023). MSC: 34G10 34B16 PDFBibTeX XMLCite \textit{A. V. Glushak}, Lobachevskii J. Math. 44, No. 8, 3298--3308 (2023; Zbl 1533.34052) Full Text: DOI
Glushak, A. V. Dirichlet problem on the half-line for an abstract Euler-Poisson-Darboux equation containing powers of an unbounded operator. (English. Russian original) Zbl 07786626 Differ. Equ. 59, No. 10, 1356-1371 (2023); translation from Differ. Uravn. 59, No. 10, 1357-1372 (2023). Reviewer: Marko Kostić (Novi Sad) MSC: 34G10 34B40 34D05 47D06 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equ. 59, No. 10, 1356--1371 (2023; Zbl 07786626); translation from Differ. Uravn. 59, No. 10, 1357--1372 (2023) Full Text: DOI
Glushak, A. V. Operator hypergeometric functions. (English. Russian original) Zbl 07712798 J. Math. Sci., New York 272, No. 5, 658-666 (2023); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 174, 37-45 (2020). Reviewer: Sergei V. Rogosin (Minsk) MSC: 34G10 34A05 33C20 45J05 PDFBibTeX XMLCite \textit{A. V. Glushak}, J. Math. Sci., New York 272, No. 5, 658--666 (2023; Zbl 07712798); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 174, 37--45 (2020) Full Text: DOI
Glushak, A. V. On the unique solvability of boundary value problems for an abstract Euler-Poisson-Darboux equations on a finite interval. (English) Zbl 1518.35521 Lobachevskii J. Math. 44, No. 3, 993-1002 (2023). MSC: 35Q05 34G10 33C10 35A01 PDFBibTeX XMLCite \textit{A. V. Glushak}, Lobachevskii J. Math. 44, No. 3, 993--1002 (2023; Zbl 1518.35521) Full Text: DOI
Glushak, A. V. The associated operator Legendre function and the incomplete Cauchy problem. (English. Russian original) Zbl 1525.47072 Russ. Math. 66, No. 9, 1-10 (2022); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2022, No. 9, 3-13 (2022). MSC: 47D06 34G10 26A33 PDFBibTeX XMLCite \textit{A. V. Glushak}, Russ. Math. 66, No. 9, 1--10 (2022; Zbl 1525.47072); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2022, No. 9, 3--13 (2022) Full Text: DOI
Glushak, A. V. On the solvability of initial problems for an abstract generalized Euler-Poisson-Darboux equation of higher order. (English) Zbl 1502.34069 Lobachevskii J. Math. 43, No. 6, 1313-1325 (2022). MSC: 34G10 PDFBibTeX XMLCite \textit{A. V. Glushak}, Lobachevskii J. Math. 43, No. 6, 1313--1325 (2022; Zbl 1502.34069) Full Text: DOI
Glushak, A. V. On the relationship between the solutions of an abstract Euler-Poisson-Darboux equation and fractional powers of the operator coefficient in the equation. (English. Russian original) Zbl 1496.35156 Differ. Equ. 58, No. 5, 577-592 (2022); translation from Differ. Uravn. 58, No. 5, 575-590 (2022). MSC: 35C15 34G10 47D09 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equ. 58, No. 5, 577--592 (2022; Zbl 1496.35156); translation from Differ. Uravn. 58, No. 5, 575--590 (2022) Full Text: DOI
Glushak, A. V. Uniqueness criterion for solutions of nonlocal problems on a finite interval for abstract singular equations. (English. Russian original) Zbl 1500.34053 Math. Notes 111, No. 1, 20-32 (2022); translation from Mat. Zametki 111, No. 1, 24-39 (2022). Reviewer: Nikita V. Artamonov (Moskva) MSC: 34G10 34B10 34B16 PDFBibTeX XMLCite \textit{A. V. Glushak}, Math. Notes 111, No. 1, 20--32 (2022; Zbl 1500.34053); translation from Mat. Zametki 111, No. 1, 24--39 (2022) Full Text: DOI
Glushak, A. V. Uniqueness criterion for the solution of boundary-value problems for the abstract Euler-Poisson-Darboux equation on a finite interval. (English. Russian original) Zbl 1476.34132 Math. Notes 109, No. 6, 867-875 (2021); translation from Mat. Zametki 109, No. 6, 821-831 (2021). Reviewer: Yaroslav Baranetskij (Lviv) MSC: 34G10 34B09 34B15 PDFBibTeX XMLCite \textit{A. V. Glushak}, Math. Notes 109, No. 6, 867--875 (2021; Zbl 1476.34132); translation from Mat. Zametki 109, No. 6, 821--831 (2021) Full Text: DOI
Glushak, A. V. Solvability of degenerating hyperbolic differential equations with unbounded operator coefficients. (English. Russian original) Zbl 1458.35277 Differ. Equ. 57, No. 1, 60-74 (2021); translation from Differ. Uravn. 57, No. 1, 61-75 (2021). MSC: 35L90 35L80 35L15 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equ. 57, No. 1, 60--74 (2021; Zbl 1458.35277); translation from Differ. Uravn. 57, No. 1, 61--75 (2021) Full Text: DOI
Glushak, A. V. A family of singular differential equations. (English) Zbl 1455.34062 Lobachevskii J. Math. 41, No. 5, 763-771 (2020). MSC: 34G10 34A12 34A05 PDFBibTeX XMLCite \textit{A. V. Glushak}, Lobachevskii J. Math. 41, No. 5, 763--771 (2020; Zbl 1455.34062) Full Text: DOI
Glushak, A. V. Transmutation operators as a solvability concept of abstract singular equations. (English) Zbl 1501.47079 Kravchenko, Vladislav V. (ed.) et al., Transmutation operators and applications. Cham: Birkhäuser. Trends Math., 379-409 (2020). MSC: 47E05 34G10 35Q05 44A15 47D06 PDFBibTeX XMLCite \textit{A. V. Glushak}, in: Transmutation operators and applications. Cham: Birkhäuser. 379--409 (2020; Zbl 1501.47079) Full Text: DOI
Glushak, A. V. Nonlocal problem for the abstract Bessel-Struve equation. (English. Russian original) Zbl 1502.34068 Russ. Math. 63, No. 7, 24-32 (2019); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2019, No. 7, 29-38 (2019). MSC: 34G10 PDFBibTeX XMLCite \textit{A. V. Glushak}, Russ. Math. 63, No. 7, 24--32 (2019; Zbl 1502.34068); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2019, No. 7, 29--38 (2019) Full Text: DOI
Glushak, A. V. On the solvability of boundary value problems for an abstract Bessel-Struve equation. (English. Russian original) Zbl 1451.34082 Differ. Equ. 55, No. 8, 1069-1076 (2019); translation from Differ. Uravn. 55, No. 8, 1103-1110 (2019). Reviewer: Marjeta Kramar Fijavž (Ljubljana) MSC: 34G10 34B05 47D06 47D62 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equ. 55, No. 8, 1069--1076 (2019; Zbl 1451.34082); translation from Differ. Uravn. 55, No. 8, 1103--1110 (2019) Full Text: DOI
Glushak, A. V. An operator formula for the shift of the solution of the Cauchy problem for an abstract Euler-Poisson-Darboux equation. (English. Russian original) Zbl 1431.34075 Math. Notes 105, No. 5, 649-656 (2019); translation from Mat. Zametki 105, No. 5, 656-665 (2019). Reviewer: Pham Viet Hai (Hanoi) MSC: 34G10 34A12 PDFBibTeX XMLCite \textit{A. V. Glushak}, Math. Notes 105, No. 5, 649--656 (2019; Zbl 1431.34075); translation from Mat. Zametki 105, No. 5, 656--665 (2019) Full Text: DOI
Malai, N. V.; Glushak, A. V.; Shchukin, E. R. Solution of a boundary value problem for velocity-linearized Navier-Stokes equations in the case of a heated spherical solid particle settling in fluid. (English. Russian original) Zbl 1404.35327 Comput. Math. Math. Phys. 58, No. 7, 1132-1141 (2018); translation from Zh. Vychisl. Mat. Mat. Fiz. 58, No. 7 (2018). MSC: 35Q30 76D05 35A02 80A20 PDFBibTeX XMLCite \textit{N. V. Malai} et al., Comput. Math. Math. Phys. 58, No. 7, 1132--1141 (2018; Zbl 1404.35327); translation from Zh. Vychisl. Mat. Mat. Fiz. 58, No. 7 (2018) Full Text: DOI
Glushak, A. V. Uniquely solvable problems for abstract Legendre equation. (English. Russian original) Zbl 1405.34052 Russ. Math. 62, No. 7, 1-12 (2018); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2018, No. 7, 3-15 (2018). Reviewer: Nikita V. Artamonov (Moskva) MSC: 34G10 34A12 34B10 34A05 PDFBibTeX XMLCite \textit{A. V. Glushak}, Russ. Math. 62, No. 7, 1--12 (2018; Zbl 1405.34052); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2018, No. 7, 3--15 (2018) Full Text: DOI
Glushak, A. V. Criterion for the solvability of the weighted Cauchy problem for an abstract Euler-Poisson-Darboux equation. (English. Russian original) Zbl 1403.34043 Differ. Equ. 54, No. 5, 622-632 (2018); translation from Differ. Uravn. 54, No. 5, 627-637 (2018). Reviewer: Marjeta Kramar Fijavž (Ljubljana) MSC: 34G10 34A12 47D06 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equ. 54, No. 5, 622--632 (2018; Zbl 1403.34043); translation from Differ. Uravn. 54, No. 5, 627--637 (2018) Full Text: DOI
Glushak, P. A.; Markiv, B. B.; Tokarchuk, M. V. Zubarev’s nonequilibrium statistical operator method in the generalized statistics of multiparticle systems. (English. Russian original) Zbl 1393.82015 Theor. Math. Phys. 194, No. 1, 57-73 (2018); translation from Teor. Mat. Fiz. 194, No. 1, 71-89 (2018). MSC: 82C35 82C70 82C24 94A17 PDFBibTeX XMLCite \textit{P. A. Glushak} et al., Theor. Math. Phys. 194, No. 1, 57--73 (2018; Zbl 1393.82015); translation from Teor. Mat. Fiz. 194, No. 1, 71--89 (2018) Full Text: DOI
Glushak, A. V. Abstract Cauchy problem for the Bessel-Struve equation. (English. Russian original) Zbl 1382.34065 Differ. Equ. 53, No. 7, 864-878 (2017); translation from Differ. Uravn. 53, No. 7, 891-905 (2017). Reviewer: Nikita V. Artamonov (Moskva) MSC: 34G10 34A12 47D62 47D03 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equ. 53, No. 7, 864--878 (2017; Zbl 1382.34065); translation from Differ. Uravn. 53, No. 7, 891--905 (2017) Full Text: DOI
Malaĭ, N. V.; Glushak, A. V.; Limanskaya, Anna V. Investigation of boundary-value problem for slow flow of a sphere by viscous non-isothermal gas. (English. Russian original) Zbl 1433.76147 Russ. Math. 60, No. 12, 43-53 (2016); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2016, No. 12, 54-65 (2016). MSC: 76N15 PDFBibTeX XMLCite \textit{N. V. Malaĭ} et al., Russ. Math. 60, No. 12, 43--53 (2016; Zbl 1433.76147); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2016, No. 12, 54--65 (2016) Full Text: DOI
Glushak, A. V. Abstract Euler-Poisson-Darboux equation with nonlocal condition. (English. Russian original) Zbl 1380.34092 Russ. Math. 60, No. 6, 21-28 (2016); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2016, No. 6, 27-35 (2016). Reviewer: Miklavž Mastinšek (Maribor) MSC: 34G10 34B10 PDFBibTeX XMLCite \textit{A. V. Glushak}, Russ. Math. 60, No. 6, 21--28 (2016; Zbl 1380.34092); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2016, No. 6, 27--35 (2016) Full Text: DOI
Glushak, A. V.; Pokruchin, O. A. Criterion for the solvability of the Cauchy problem for an abstract Euler-Poisson-Darboux equation. (English. Russian original) Zbl 1345.35069 Differ. Equ. 52, No. 1, 39-57 (2016); translation from Differ. Uravn. 52, No. 1, 41-59 (2016). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 35Q05 26A33 34K06 PDFBibTeX XMLCite \textit{A. V. Glushak} and \textit{O. A. Pokruchin}, Differ. Equ. 52, No. 1, 39--57 (2016; Zbl 1345.35069); translation from Differ. Uravn. 52, No. 1, 41--59 (2016) Full Text: DOI
Glushak, A. V.; Avad, H. K. On the solvability of an abstract differential equation of fractional order with a variable operator. (English. Russian original) Zbl 1317.34011 J. Math. Sci., New York 202, No. 5, 637-652 (2014); translation from Sovrem. Mat., Fundam. Napravl. 47, 18-32 (2013). MSC: 34A08 34G10 34A12 PDFBibTeX XMLCite \textit{A. V. Glushak} and \textit{H. K. Avad}, J. Math. Sci., New York 202, No. 5, 637--652 (2014; Zbl 1317.34011); translation from Sovrem. Mat., Fundam. Napravl. 47, 18--32 (2013) Full Text: DOI
Popova, V. A.; Glushak, A. V. The inverse problem for a singular evolution equation with nonlocal boundary condition. (Russian. English summary) Zbl 1326.34094 Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2012, No. 1, 182-186 (2012). MSC: 34G10 34B10 34A55 PDFBibTeX XMLCite \textit{V. A. Popova} and \textit{A. V. Glushak}, Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2012, No. 1, 182--186 (2012; Zbl 1326.34094)
Glushak, A. V.; Malaj, N. V.; Mironova, N. N. Boundary value problem for the Navier-Stokes equations linearized in rate in the case of non-isothermal flow of heated gaseous medium spheroid. (Russian) Zbl 1274.35267 Zh. Vychisl. Mat. Mat. Fiz. 52, No. 5, 946-959 (2012). Reviewer: Andrei Zemskov (Moskva) MSC: 35Q30 PDFBibTeX XMLCite \textit{A. V. Glushak} et al., Zh. Vychisl. Mat. Mat. Fiz. 52, No. 5, 946--959 (2012; Zbl 1274.35267) Full Text: MNR
Malai, N. V.; Mironova, N. N.; Glushak, A. V. Solution of the boundary value problem for the Navier-Stokes equation for the flow of a gaseous medium past a heated spheroid. (English. Russian original) Zbl 1256.35063 Differ. Equ. 48, No. 6, 886-890 (2012); translation from Differ. Uravn. 48, No. 6, 879-883 (2012). MSC: 35Q30 35Q79 76N15 35A02 PDFBibTeX XMLCite \textit{N. V. Malai} et al., Differ. Equ. 48, No. 6, 886--890 (2012; Zbl 1256.35063); translation from Differ. Uravn. 48, No. 6, 879--883 (2012) Full Text: DOI
Glushak, A. V.; Manaenkova, T. A. Direct and inverse problems for an abstract differential equation containing Hadamard fractional derivatives. (English. Russian original) Zbl 1273.34067 Differ. Equ. 47, No. 9, 1307-1317 (2011); translation from Differ. Uravn. 47, No. 9, 1294-1304 (2011). MSC: 34G10 34A08 34A55 PDFBibTeX XMLCite \textit{A. V. Glushak} and \textit{T. A. Manaenkova}, Differ. Equ. 47, No. 9, 1307--1317 (2011; Zbl 1273.34067); translation from Differ. Uravn. 47, No. 9, 1294--1304 (2011) Full Text: DOI
Avad, Kh. K.; Glushak, A. V. Quasi-inversion method for an evolutionary equation of fractional order. (English. Russian original) Zbl 1219.35346 J. Math. Sci., New York 173, No. 2, 172-180 (2011); translation from Sovrem. Mat. Prilozh. 67 (2010). MSC: 35R11 PDFBibTeX XMLCite \textit{Kh. K. Avad} and \textit{A. V. Glushak}, J. Math. Sci., New York 173, No. 2, 172--180 (2011; Zbl 1219.35346); translation from Sovrem. Mat. Prilozh. 67 (2010) Full Text: DOI
Avad, H. K.; Glushak, A. V. On perturbations of abstract fractional differential equations by nonlinear operators. (English. Russian original) Zbl 1305.34007 J. Math. Sci., New York 170, No. 3, 306-323 (2010); translation from Sovrem. Mat., Fundam. Napravl. 35, 5-21 (2010). MSC: 34A08 34G20 34A12 34D10 34A55 PDFBibTeX XMLCite \textit{H. K. Avad} and \textit{A. V. Glushak}, J. Math. Sci., New York 170, No. 3, 306--323 (2010; Zbl 1305.34007); translation from Sovrem. Mat., Fundam. Napravl. 35, 5--21 (2010) Full Text: DOI
Glushak, A. V. Inverse problems for evolution equations with fractional integrals at boundary-value conditions. (English. Russian original) Zbl 1300.34037 J. Math. Sci., New York 164, No. 4, 518-530 (2010); translation from Sovrem. Mat., Fundam. Napravl. 29, 49-61 (2008). MSC: 34A55 34A08 34G10 34B10 PDFBibTeX XMLCite \textit{A. V. Glushak}, J. Math. Sci., New York 164, No. 4, 518--530 (2010; Zbl 1300.34037); translation from Sovrem. Mat., Fundam. Napravl. 29, 49--61 (2008) Full Text: DOI
Glushak, A. V. On an inverse problem for an abstract differential equation of fractional order. (English. Russian original) Zbl 1280.34014 Math. Notes 87, No. 5, 654-662 (2010); translation from Mat. Zametki 87, No. 5, 684-693 (2010). Reviewer: Krishnan Balachandran (Coimbatore) MSC: 34A55 34A08 34G10 PDFBibTeX XMLCite \textit{A. V. Glushak}, Math. Notes 87, No. 5, 654--662 (2010; Zbl 1280.34014); translation from Mat. Zametki 87, No. 5, 684--693 (2010) Full Text: DOI
Avad, Kh. K.; Glushak, A. V. Perturbation of an abstract differential equation containing fractional Riemann-Liouville derivatives. (English. Russian original) Zbl 1214.34004 Differ. Equ. 46, No. 6, 867-881 (2010); translation from Differ. Uravn. 46, No. 6, 859-873 (2010). Reviewer: Gaston M. N’Guerekata (Baltimore) MSC: 34A08 34G10 34A12 PDFBibTeX XMLCite \textit{Kh. K. Avad} and \textit{A. V. Glushak}, Differ. Equ. 46, No. 6, 867--881 (2010; Zbl 1214.34004); translation from Differ. Uravn. 46, No. 6, 859--873 (2010) Full Text: DOI
Glushak, A. V. Correctness of Cauchy-type problems for abstract differential equations with fractional derivatives. (English. Russian original) Zbl 1177.47090 Russ. Math. 53, No. 9, 10-19 (2009); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 9, 13-24 (2009). Reviewer: Stefan G. Samko (Faro) MSC: 47N20 26A33 34G10 35R20 PDFBibTeX XMLCite \textit{A. V. Glushak}, Russ. Math. 53, No. 9, 10--19 (2009; Zbl 1177.47090); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 9, 13--24 (2009) Full Text: DOI
Glushak, A. V. On the properties of a Cauchy-type problem for an abstract differential equation with fractional derivatives. (English. Russian original) Zbl 1160.34053 Math. Notes 82, No. 5, 596-607 (2007); translation from Mat. Zametki 82, No. 5, 665-677 (2007). Reviewer: Neville Ford (Chester) MSC: 34G10 34A05 26A33 47D09 47N20 35R20 PDFBibTeX XMLCite \textit{A. V. Glushak}, Math. Notes 82, No. 5, 596--607 (2007; Zbl 1160.34053); translation from Mat. Zametki 82, No. 5, 665--677 (2007) Full Text: DOI
Glushak, A. V.; Karakeev, T. T. Numerical solution of the linear inverse problem for the Euler-Darboux equation. (Russian. English summary) Zbl 07811608 Zh. Vychisl. Mat. Mat. Fiz. 46, No. 5, 848-857 (2006); translation in Comput. Math. Math. Phys. 46, No. 5, 810-819 (2006). MSC: 65-XX 35R30 PDFBibTeX XMLCite \textit{A. V. Glushak} and \textit{T. T. Karakeev}, Zh. Vychisl. Mat. Mat. Fiz. 46, No. 5, 848--857 (2006; Zbl 07811608); translation in Comput. Math. Math. Phys. 46, No. 5, 810--819 (2006) Full Text: DOI MNR
Glushak, A. V. On the relationship between the integrated cosine function and the operator Bessel function. (English. Russian original) Zbl 1123.34324 Differ. Equ. 42, No. 5, 619-626 (2006); translation from Differ. Uravn. 42, No. 5, 583-589 (2006). MSC: 34G10 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equ. 42, No. 5, 619--626 (2006; Zbl 1123.34324); translation from Differ. Uravn. 42, No. 5, 583--589 (2006) Full Text: DOI
Glushak, A. V.; Karakeev, T. T. Regularization of Volterra integral equations of the third order and inverse problems for Euler-Darboux equations. (Russian. English summary) Zbl 1381.35244 Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2005, No. 2, 124-127 (2005). MSC: 35R30 35L20 45Q05 65L09 65R32 65R20 45D05 PDFBibTeX XMLCite \textit{A. V. Glushak} and \textit{T. T. Karakeev}, Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2005, No. 2, 124--127 (2005; Zbl 1381.35244)
Glushak, A. V. Cauchy-type problem for an abstract differential equation with fractional derivatives. (English. Russian original) Zbl 1086.34050 Math. Notes 77, No. 1, 26-38 (2005); translation from Mat. Zametki 77, No. 1, 28-41 (2005). Reviewer: Samir B. Hadid (Ajman) MSC: 34G10 26A33 PDFBibTeX XMLCite \textit{A. V. Glushak}, Math. Notes 77, No. 1, 26--38 (2005; Zbl 1086.34050); translation from Mat. Zametki 77, No. 1, 28--41 (2005) Full Text: DOI
Glushak, A. V. On periodic solutions of abstract differential equation with fractional derivative. (Russian. English summary) Zbl 1418.34121 Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2003, No. 1, 96-98 (2003). MSC: 34G20 34G10 34C25 26A33 PDFBibTeX XMLCite \textit{A. V. Glushak}, Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2003, No. 1, 96--98 (2003; Zbl 1418.34121)
Glushak, A. V. Properties of solutions of equations containing powers of an unbounded operator. (English. Russian original) Zbl 1083.34044 Differ. Equ. 39, No. 10, 1428-1439 (2003); translation from Differ. Uravn. 39, No. 10, 1355-1365 (2003). Reviewer: Cristinel Mortici (Targoviste) MSC: 34G10 34A12 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equ. 39, No. 10, 1428--1439 (2003; Zbl 1083.34044); translation from Differ. Uravn. 39, No. 10, 1355--1365 (2003) Full Text: DOI
Glushak, A. V. On a formula for solutions of an abstract differential equation containing fractional derivatives. (Russian. English summary) Zbl 1165.34385 Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2002, No. 2, 56-58 (2002). MSC: 34G10 34A05 26A33 PDFBibTeX XMLCite \textit{A. V. Glushak}, Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2002, No. 2, 56--58 (2002; Zbl 1165.34385)
Glushak, A. V. On a problem of Cauchy-type for an inhomogeneous abstract differential equation with fractional derivative. (Russian. English summary) Zbl 1088.34531 Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2002, No. 1, 121-123 (2002). MSC: 34G10 26A33 34A12 PDFBibTeX XMLCite \textit{A. V. Glushak}, Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2002, No. 1, 121--123 (2002; Zbl 1088.34531)
Glushak, A. V. The problem of Cauchy-type for an abstract differential equation with fractional derivative. (Russian. English summary) Zbl 1061.34041 Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2001, No. 2, 74-77 (2001). Reviewer: Klaus R. Schneider (Berlin) MSC: 34G10 34A12 26A33 PDFBibTeX XMLCite \textit{A. V. Glushak}, Vestn. Voronezh. Gos. Univ., Ser. Fiz. Mat. 2001, No. 2, 74--77 (2001; Zbl 1061.34041)
Glushak, A. V. Stabilization of the solution of the Cauchy problem for an abstract differential equation of first order. (English. Russian original) Zbl 1036.34071 Russ. Math. 45, No. 11, 1-11 (2001); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2001, No. 11, 3-13 (2001). Reviewer: Irina V. Melnikova (MR 2003d:34116) MSC: 34G10 34D05 47D06 PDFBibTeX XMLCite \textit{A. V. Glushak}, Russ. Math. 45, No. 11, 1--11 (2001; Zbl 1036.34071); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2001, No. 11, 3--13 (2001)
Glushak, A. V. The Legendre operator function. (English. Russian original) Zbl 1047.34066 Izv. Math. 65, No. 6, 1073-1083 (2001); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 65, No. 6, 3-14 (2001). Reviewer: Miklavž Mastinšek (Maribor) MSC: 34G10 47D06 PDFBibTeX XMLCite \textit{A. V. Glushak}, Izv. Math. 65, No. 6, 1073--1083 (2001; Zbl 1047.34066); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 65, No. 6, 3--14 (2001) Full Text: DOI
Vorob’eva, S. A.; Glushak, A. V. An abstract Euler-Poisson-Darboux equation containing powers of an unbounded operator. (English. Russian original) Zbl 1001.34048 Differ. Equ. 37, No. 5, 743-746 (2001); translation from Differ. Uravn. 37, No. 5, 706-709 (2001). Reviewer: I.J.Mardanov (Baku) MSC: 34G10 47N20 PDFBibTeX XMLCite \textit{S. A. Vorob'eva} and \textit{A. V. Glushak}, Differ. Equ. 37, No. 5, 743--746 (2001; Zbl 1001.34048); translation from Differ. Uravn. 37, No. 5, 706--709 (2001) Full Text: DOI
Glushak, A. V. Iterated Cauchy and Dirichlet problems with the Bessel operator in Banach space. (English. Russian original) Zbl 0988.34046 Russ. Math. 43, No. 8, 1-8 (1999); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1999, No. 8, 3-10 (1999). Reviewer: Uljana A.Anufrieva (MR 2001g:34082) MSC: 34G10 PDFBibTeX XML
Glushak, A. V. Regular and singular perturbations of an abstract Euler-Poisson-Darboux equation. (English. Russian original) Zbl 0968.34041 Math. Notes 66, No. 3, 292-298 (1999); translation from Mat. Zametki 66, No. 3, 364-371 (1999). MSC: 34G10 PDFBibTeX XMLCite \textit{A. V. Glushak}, Math. Notes 66, No. 3, 292--298 (1999; Zbl 0968.34041); translation from Mat. Zametki 66, No. 3, 364--371 (1999) Full Text: DOI
Glushak, A. V. The operator Bessel function, related semigroups, and the modified Hilbert transform. (English. Russian original) Zbl 0935.34054 Differ. Equations 35, No. 1, 130-132 (1999); translation from Differ. Uravn. 35, No. 1, 128-130 (1999). MSC: 34G20 47H20 44A15 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equations 35, No. 1, 130--132 (1999; Zbl 0935.34054); translation from Differ. Uravn. 35, No. 1, 128--130 (1999)
Glushak, A. V. On a first-order linear inhomogeneous equation with a singularity. (English. Russian original) Zbl 1122.34326 Differ. Equations 34, No. 9, 1285-1287 (1998); translation from Differ. Uravn. 34, No. 9, 1284-1285 (1998). MSC: 34G10 47D06 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equations 34, No. 9, 1285--1287 (1998; Zbl 1122.34326); translation from Differ. Uravn. 34, No. 9, 1284--1285 (1998)
Glushak, A. V. The Bessel operator function. (English. Russian original) Zbl 0965.34052 Dokl. Math. 55, No. 1, 103-105 (1997); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 352, No. 5, 587-589 (1997). MSC: 34G10 47D09 34K30 47D06 47N20 PDFBibTeX XMLCite \textit{A. V. Glushak}, Dokl. Math. 55, No. 1, 587--589 (1997; Zbl 0965.34052); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 352, No. 5, 587--589 (1997)
Glushak, A. V. Stabilization of a solution of the Dirichlet problem for an elliptic equation in a Banach space. (English. Russian original) Zbl 0907.34044 Differ. Equations 33, No. 4, 513-517 (1997); translation from Differ. Uravn. 33, No. 4, 510-514 (1997). Reviewer: V.Chernyatin (Szczecin) MSC: 34G10 47F05 35J05 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equations 33, No. 4, 513--517 (1997; Zbl 0907.34044); translation from Differ. Uravn. 33, No. 4, 510--514 (1997)
Glushak, A. V. On the asymptotic proximity of the solutions of a Cauchy problem for first-order differential equations in a Banach space. (English. Russian original) Zbl 0906.34044 Russ. Math. 41, No. 7, 14-17 (1997); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1997, No. 7 (422), 12-15 (1997). Reviewer: G.Karakostas (Ioannina) MSC: 34G10 PDFBibTeX XMLCite \textit{A. V. Glushak}, Russ. Math. 41, No. 7, 14--17 (1997; Zbl 0906.34044); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1997, No. 7 (422), 12--15 (1997)
Glushak, A. V.; Orsingher, E. General solution of a hyperbolic equation arising in the study of motion with random acceleration. (English. Russian original) Zbl 0927.60096 Theory Probab. Math. Stat. 55, 49-53 (1997); translation from Teor. Jmovirn. Mat. Stat. 55, 50-54 (1996). Reviewer: N.M.Zinchenko (Kyïv) MSC: 60K99 PDFBibTeX XMLCite \textit{A. V. Glushak} and \textit{E. Orsingher}, Teor. Ĭmovirn. Mat. Stat. 55, 50--54 (1996; Zbl 0927.60096); translation from Teor. Jmovirn. Mat. Stat. 55, 50--54 (1996)
Glushak, A. V. Perturbations of an abstract Euler-Poisson-Darboux equation. (English. Russian original) Zbl 0898.34057 Math. Notes 60, No. 3, 269-273 (1996); translation from Mat. Zametki 60, No. 3, 363-369 (1996). MSC: 34G20 35Q05 PDFBibTeX XMLCite \textit{A. V. Glushak}, Math. Notes 60, No. 3, 269--273 (1996; Zbl 0898.34057); translation from Mat. Zametki 60, No. 3, 363--369 (1996) Full Text: DOI
Glushak, A. V. Integral representation and stabilization of the solution to the Cauchy problem for an equation with two noncommuting operators. (English. Russian original) Zbl 0852.35028 Math. Notes 58, No. 1, 703-709 (1995); translation from Mat. Zametki 58, No. 1, 38-47 (1995). MSC: 35C15 47D06 34G10 PDFBibTeX XMLCite \textit{A. V. Glushak}, Math. Notes 58, No. 1, 703--709 (1995; Zbl 0852.35028); translation from Mat. Zametki 58, No. 1, 38--47 (1995) Full Text: DOI
Glushak, A. V. On certain abstract Euler-Poisson-Darboux equation with the lowest term containing a singularity. (English. Russian original) Zbl 0855.34072 Russ. Math. 39, No. 3, 1-5 (1995); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1995, No. 3(394), 3-7 (1995). Reviewer: R.Kodnár (Bratislava) MSC: 34G20 35Q05 PDFBibTeX XMLCite \textit{A. V. Glushak}, Russ. Math. 39, No. 3, 3--7 (1995; Zbl 0855.34072); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1995, No. 3(394), 3--7 (1995)
Glushak, A. V. A necessary and sufficient stabilization condition for the solution to the Cauchy problem for an equation with operator coefficients. (English. Russian original) Zbl 0852.34061 Differ. Equations 30, No. 7, 1030-1036 (1994); translation from Differ. Uravn. 30, No. 7, 1111-1117 (1994). Reviewer: V.Chernyatin (Szczecin) MSC: 34G10 34A12 PDFBibTeX XMLCite \textit{A. V. Glushak}, Differ. Equations 30, No. 7, 1030--1036 (1994; Zbl 0852.34061); translation from Differ. Uravn. 30, No. 7, 1111--1117 (1994)
Glushak, A. V.; Shmulevich, S. D. Integral representation of solutions for one singular equation containing the sum of commuting operators. (English. Russian original) Zbl 0829.34046 Differ. Equations 28, No. 5, 676-682 (1992); translation from Differ. Uravn. 28, No. 5, 831-838 (1992). Reviewer: Ivan Straškraba (Praha) MSC: 34G10 34A05 PDFBibTeX XMLCite \textit{A. V. Glushak} and \textit{S. D. Shmulevich}, Differ. Equations 28, No. 5, 831--838 (1992; Zbl 0829.34046); translation from Differ. Uravn. 28, No. 5, 831--838 (1992)
Glushak, A. V.; Repnikov, V. D. On stabilization of a solution of the Cauchy problem for a first-order differential equation in a Banach space. (English. Russian original) Zbl 0796.34040 Russ. Acad. Sci., Dokl., Math. 46, No. 2, 245-247 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 326, No. 2, 224-226 (1992). Reviewer: S.I.Trofimchuk (Kiev) MSC: 34G10 34C11 35K99 35Q05 PDFBibTeX XMLCite \textit{A. V. Glushak} and \textit{V. D. Repnikov}, Russ. Acad. Sci., Dokl., Math. 46, No. 2, 1 (1992; Zbl 0796.34040); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 326, No. 2, 224--226 (1992)
Glushak, B. L.; Kuropatenko, V. F.; Novikov, S. A. Research on the strength of materials under dynamic loads. (Issledovanie prochnosti materialov pri dinamicheskikh nagruzkakh.) (Russian) Zbl 0857.73002 Novosibirsk: Nauka. 295 p. (1992). MSC: 74-02 74Axx 74-05 74M20 74R99 PDFBibTeX XMLCite \textit{B. L. Glushak} et al., Issledovanie prochnosti materialov pri dinamicheskikh nagruzkakh (Russian). Novosibirsk: Nauka (1992; Zbl 0857.73002)
Glushak, A. V.; Transirico, M.; Troisi, M. Embedding theorems for elliptic equations in unbounded domains. (Italian. English summary) Zbl 0763.35028 Rend. Mat. Appl., VII. Ser. 9, No. 1, 113-130 (1989). Reviewer: J.J.Manfredi (Pittsburgh) MSC: 35J25 46E35 PDFBibTeX XMLCite \textit{A. V. Glushak} et al., Rend. Mat. Appl., VII. Ser. 9, No. 1, 113--130 (1989; Zbl 0763.35028)
Glushak, A. V.; Shmulevich, S. D. On a degenerate parabolic equation in Banach space. (Russian) Zbl 0628.35050 Operator equations in functional spaces, Interuniv. Collect. sci. Works, Voronezh 1986, 19-24 (1986). Reviewer: K.Barckow MSC: 35K65 35C15 35B40 PDFBibTeX XML
Glushak, A. V.; Shmulevich, S. D. On some correct problems for parabolic equations of high order degenerating in the time variable. (Russian) Zbl 0616.35046 Differ. Uravn. 22, No. 6, 1065-1068 (1986). Reviewer: A.Martynyuk MSC: 35K65 35A08 35G10 35K25 PDFBibTeX XMLCite \textit{A. V. Glushak} and \textit{S. D. Shmulevich}, Differ. Uravn. 22, No. 6, 1065--1068 (1986; Zbl 0616.35046)
Glushak, A. V.; Kononenko, V. I.; Shmulevich, S. D. A singular abstract Cauchy problem. (English. Russian original) Zbl 0613.34047 Sov. Math. 30, No. 6, 78-81 (1986); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 6(289), 55-56 (1986). Reviewer: S.Aizicovici MSC: 34G10 34A12 PDFBibTeX XMLCite \textit{A. V. Glushak} et al., Sov. Math. 30, No. 6, 78--81 (1986; Zbl 0613.34047); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 6(289), 55--56 (1986)
Glushak, A. V. A degenerate elliptic-parabolic equation in an unbounded domain. (English) Zbl 0325.35042 Sib. Math. J. 16(1975), 530-535 (1976). MSC: 35J70 35B45 PDFBibTeX XMLCite \textit{A. V. Glushak}, Sib. Math. J. 16, 530--535 (1976; Zbl 0325.35042) Full Text: DOI
Glushak, A. V. Solvability of the Dirichlet problem for a degenerate equation in a sector of the plane. (English. Russian original) Zbl 0326.35036 Sov. Math., Dokl. 16, 1014-1018 (1975); translation from Dokl. Akad. Nauk SSSR 223, 1048-1051 (1975). MSC: 35J70 35J25 PDFBibTeX XMLCite \textit{A. V. Glushak}, Sov. Math., Dokl. 16, 1014--1018 (1975; Zbl 0326.35036); translation from Dokl. Akad. Nauk SSSR 223, 1048--1051 (1975)
Glushak, A. V. Über eine entartete elliptisch-parabolische Gleichung im unbeschränkten Gebiet. (Russian) Zbl 0316.35042 Sib. Mat. Zh. 16, 691-699 (1975). MSC: 35J70 35B45 PDFBibTeX XMLCite \textit{A. V. Glushak}, Sib. Mat. Zh. 16, 691--699 (1975; Zbl 0316.35042)