On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
-
Shota Akhalaia
und
Mzia Talakhadze
Abstract
The well-posed problem for a nonlocal boundary value problem is considered for a singular system of linear generalized ordinary differential equations. The considered system is analogous to the system corresponding to the n-order ordinary differential equation. Along with the standard well-posed question, there is considered the so-called conditionally well-posed one. The effective sufficient conditions are established for both problems.
References
[1] M. Ashordia, On the correctness of linear boundary value problems for systems of generalized ordinary differential equations, Georgian Math. J. 1 (1994), no. 4, 343–351. 10.1007/BF02307443Suche in Google Scholar
[2] M. Ashordia, On the correctness of nonlinear boundary value problems for systems of generalized ordinary differential equations, Georgian Math. J. 3 (1996), no. 6, 501–524. 10.1007/BF02259778Suche in Google Scholar
[3] M. Ashordia, Criteria of correctness of linear boundary value problems for systems of generalized ordinary differential equations, Czechoslovak Math. J. 46(121) (1996), no. 3, 385–404. 10.21136/CMJ.1996.127304Suche in Google Scholar
[4] M. Ashordia, On the general and multipoint boundary value problem for linear systems of generalized ordinary differential equations, linear impulsive and linear difference systems, Mem. Differ. Equ. Math. Phys. 36 (2005), 1–80. Suche in Google Scholar
[5] M. T. Ashordia, On boundary value problems for systems of linear generalized ordinary differential equations with singularities (in Russian), Differ. Uravn. 42 (2006), no. 3, 291–301; translation in Differ. Equ. 42 (2006), no. 3, 307–319. 10.1134/S0012266106030013Suche in Google Scholar
[6] M. T. Ashordia, On some boundary value problems for linear generalized differential systems with singularities (in Russian), Differ. Uravn. 46 (2010), no. 2, 163–177; translation in Differ. Equ. 46 (2010), no. 2, 167–181. 10.1134/S0012266110020023Suche in Google Scholar
[7] M. Ashordia, On two-point singular boundary value problems for systems of linear generalized ordinary differential equations, Mem. Differ. Equ. Math. Phys. 56 (2012), 9–35. Suche in Google Scholar
[8] M. Ashordia, On conditions for the well-posedness pf nonlocal problem for a class of linear generalized ordinary differential equations with singularities, Mem. Differ. Equ. Math. Phys. 59 (2013), 105–112. Suche in Google Scholar
[9] M. Ashordia, The general boundary value problems for linear systems of generalized ordinary differential equations, linear impulsive differential and ordinary differential systems. Numerical solvability, Mem. Differ. Equ. Math. Phys. 81 (2020), 1–184. Suche in Google Scholar
[10] T. H. Hildebrandt, On systems of linear differentio-Stieltjes-integral equations, Illinois J. Math. 3 (1959), 352–373. 10.1215/ijm/1255455257Suche in Google Scholar
[11] I. T. Kiguradze, Some Singular Boundary Value Problems for Ordinary Differential Equations (in Russian), Izdat. Tbilis. Univ., Tbilisi, 1975. Suche in Google Scholar
[12] I. Kiguradze, The Initial Value Problem and Boundary Value Problems for Systems of Ordinary Differential Equations. Vol. I. Linear Theory (in Russian), “Metsniereba”, Tbilisi, 1997. Suche in Google Scholar
[13] I. Kiguradze and T. Kiguradze, Conditions for the well-posedness of nonlocal problems for higher order linear differential equations with singularities, Georgian Math. J. 18 (2011), no. 4, 735–760. 10.1515/GMJ.2011.0040Suche in Google Scholar
[14] T. Kiguradze, On some nonlocal boundary value problems for linear singular differential equations of higher order, Mem. Differ. Equ. Math. Phys. 47 (2009), 169–173. Suche in Google Scholar
[15] T. I. Kiguradze, On conditions for the well-posedness of linear singular boundary value problems (in Russian), Differ. Uravn. 46 (2010), no. 2, 183–190; translation in Differ. Equ. 46 (2010), no. 2, 187–194. Suche in Google Scholar
[16] J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J. 7 (1957), no. 3, 418–449. 10.21136/CMJ.1957.100258Suche in Google Scholar
[17] G. A. Monteiro, A. Slavík and M. Tvrdý, Kurzweil–Stieltjes Integral. Theory and Applications, Ser. Real Anal. 15, World Scientific, Hackensack, 2019. Suche in Google Scholar
[18] Š. Schwabik and M. Tvrdý, Boundary value problems for generalized linear differential equations, Czechoslovak Math. J. 29(104) (1979), no. 3, 451–477. 10.21136/CMJ.1979.101627Suche in Google Scholar
[19] Š. Schwabik, M. Tvrdý and O. Vejvoda, Differential and Integral Equations. Boundary Value Problems and Adjoints, D. Reidel, Dordrecht, 1979. Suche in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
- Products of Toeplitz operators with angular symbols
- Characterization of Lie-type higher derivations of triangular rings
- On classifying map of the integral Krichever–Hoehn formal group law
- Demicompactness perturbation in Banach algebras and some stability results
- On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
- On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
- Asymptotic behaviors of solutions of a class of time-varying differential equations
- Fekete–Szegő problem of strongly α-close-to-convex functions associated with generalized fractional operator
- Some properties of Vitali sets
- Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
- Generalized derivations with Engel condition on Lie ideals of prime rings
- Attractivity of implicit differential equations with composite fractional derivative
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
Artikel in diesem Heft
- Frontmatter
- On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
- Products of Toeplitz operators with angular symbols
- Characterization of Lie-type higher derivations of triangular rings
- On classifying map of the integral Krichever–Hoehn formal group law
- Demicompactness perturbation in Banach algebras and some stability results
- On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
- On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
- Asymptotic behaviors of solutions of a class of time-varying differential equations
- Fekete–Szegő problem of strongly α-close-to-convex functions associated with generalized fractional operator
- Some properties of Vitali sets
- Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
- Generalized derivations with Engel condition on Lie ideals of prime rings
- Attractivity of implicit differential equations with composite fractional derivative
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
