Linear overdetermined boundary value problems in Hilbert space. (English) Zbl 1308.34100
Summary: The general linear boundary value problem for an abstract functional differential equation is considered in the case that the number of boundary conditions is greater than the dimension of the null-space to the corresponding homogeneous equation. Sufficient conditions of the solvability of the problem are obtained. A case of a functional differential system with aftereffect is considered separately.
MSC:
| 34K30 | Functional-differential equations in abstract spaces |
| 34K10 | Boundary value problems for functional-differential equations |
| 34K06 | Linear functional-differential equations |
References:
| [1] | Nayfeh, AN, Mook, DT: Nonlinear Oscillations. Wiley, New York (1970) |
| [2] | Maksimov, VP, Rumyantsev, AN: Boundary value problems and problems of pulse control in economic dynamics: constructive study. Russ. Math. 37, 48-62 (1993) · Zbl 0835.90017 |
| [3] | Boichuk, AA: Constructive Methods of Analysis of Boundary Value Problems. Naukova Dumka, Kyiv (1990) · Zbl 0786.34029 |
| [4] | Azbelev, NV, Rakhmatullina, LF: Theory of linear abstract functional differential equations and applications. Mem. Differ. Equ. Math. Phys. 8, 1-102 (1996) · Zbl 0870.34067 |
| [5] | Azbelev, NV, Maksimov, VP, Rakhmatullina, LF: Introduction to the Theory of Functional Differential Equations. Nauka, Moscow (1991) · Zbl 0725.34071 |
| [6] | Maksimov, VP; Agarwal, R. (ed.); Perera, K. (ed.), Theory of functional differential equations and some problems in economic dynamics, 757-765 (2006), New York · Zbl 1149.34349 |
| [7] | Azbelev, NV, Maksimov, VP, Simonov, PM: Theory of functional differential equations and applications. Int. J. Pure Appl. Math. 69, 203-235 (2011) · Zbl 1228.34001 |
| [8] | Azbelev, NV, Maksimov, VP, Rakhmatullina, LF: Introduction to the Theory of Functional Differential Equations: Methods and Applications. Hindawi Publishing Corporation, New York (2007) · Zbl 1202.34002 · doi:10.1155/9789775945495 |
| [9] | Azbelev, NV, Maksimov, VP, Rakhmatullina, LF: Elements of the Contemporary Theory of Functional Differential Equations. Methods and Applications. Institute of Computer-Assisted Studies, Moscow (2002) |
| [10] | Maksimov, VP; Rumyantsev, AN; Uvarova, L. (ed.); Latyshev, A. (ed.), Reliable computing experiment in the study of generalized controllability of linear functional differential systems, 91-98 (2002), New York |
| [11] | Maksimov, VP: Cauchy’s formula for a functional-differential equation. Differ. Equ. 13, 405-409 (1977) · Zbl 0398.34059 |
| [12] | Maksimov, VP: Questions of the General Theory of Functional Differential Equations. Perm State University, Perm (2003) |
| [13] | Rumyantsev, AN: Reliable Computing Experiment in the Study of Boundary Value Problems. Perm State University, Perm (1999) |
| [14] | Maksimov, VP, Chadov, AL: The constructive investigation of boundary-value problems with approximate satisfaction of boundary conditions. Russ. Math. 54, 71-74 (2010) · Zbl 1209.34078 · doi:10.3103/S1066369X10100105 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
