journal.isu.ru

Начальная страница

Конечная страница

УДК

Раздел
     

Файл
Скачать Изменить файл

Название RU

Авторы RU

Аннотация RU
<p>Рассматривается редукция вырожденных дифференциально-разностных уравнений с фредгольмовым оператором при главной части к регулярным задачам. Показано, что выбор начальных условий связан с жордановой структурой операторных коэффицинтов уравнений. Решена задача выбора начальных условий. Доказаны теоремы существования и единственности для задач с заданными начальными условиями. Полученные результаты используются для постановки и исследования граничных задач для дифференциальных уравнений в частных производных и разностных уравнений с вырождением.</p>

Ключевые слова RU

Литература RU

Название EN

Авторы EN

Аннотация EN
<p>We consider the reduction of the degenerate difference-differential equations with Fredholm operator in the main expression to the regular problems. It is shown how the question of the choice of boundary conditions is connected with the Jordan structure of operator coefficients of the equations. The problem of the choice of boundary conditions is solved. The theorems of existence and uniqueness of boundary value problems are proved. The abstract theorems are used for statement and investigation of boundary value problems for partial differential equations and difference equations with degeneration.</p>

Ключевые слова EN

Литература EN
1. Ahmedov K.T. Analytical Method by Nekrasov-Nazarov in Nonlinear Analysis // Uspekhi Mat.Nauk. —1957. — v. 12, No 4. — P. 135–155. 2. Bitsadze K.T. Some Classes of Partial Differential Equations, ”Nauka”, Moscow. — 1981. 3. Benedetto E.Di, Showalter R.E. Implicit degenerate evolution equations and their applications // SIAM J.Math.Anal. 1981, v.12, N5 —p. 731–751. 4. B.V.Loginov B.V., Rusak Ju.B. Generalized Jordan Structure in the Problem of the Stability of Bifurcating Solutions // Nonlinear Analysis, Theory, Methods and Applications, vol.17, 3,1991. — p.219–232. 5. Nashed M.Zuhair Generalized Inverses and Applications (Proc.Adv.Sem., Madison, Wisc., 1973), Academic Press, New York, 1976. 6. Sidorov N.A.,Blagodatskaya E.B. Differential Equations with Fredholm Operator in the Leading Differential Expression // Soviet Math. Dokl., Vol. 44 (1992), No.1 — p.302–305. 7. Sidorov N.A.,Romanova O.A. Differentsial’nye Uravneniya 19 (1983) —p. 1516–1526; English transl.in Differential Equations 19 (1983). 8. Sidorov N.A., Falaleev M.V.// Differentsial’nye Uravneniya 23 (1987) —p. 726–728. (Russian) 9. Sidorov N.A.,Blagodatskaya E.B. Differential Equations with a Fredholm Operator in the Leading Differential Expression // Preprint no.1. Ac.Sci. USSR, SB ICC, 1991. 10. Sidorov N.A.,Romanova O.A. Differential Equations with the Operator of Finite Index in the Main Part // Differentsial’nye Uravneniya 30 (1994) —p.729–731. 11. Sidorov N.A. On the Branching of Solutions of the Cauchy Problem for one Class of Nonlinear Integro-differential Equations // Differentsial’nye Uravneniya 9 (1967) —p. 1592–1601. 12. Sidorov N.A. General Questions of Regularization in the Problems of Bifurcation Theory // Irkutsk university, 1982 — p.312. 13. Sidorov N.A. Solution of the Cauchy Problem for one Class of Nonlinear Integrodifferential Equations with Analytical Nonlinearities // Differentsial’nye Uravneniya 7 (1968) —p. 1309–1316. 14. Sidorov N.A. Investigation of Continuous Solutions of the Cauchy Problem in the Neighborhood of a Bifurcation Point// Izv. Vuzov; Mathematics 9 (1976) — p.99–110. 15. Sidorov N.A. On the Branching of Solutions of Differential Equations with Degeneration// Differentsial’nye Uravneniya 8 (1973) — p.1464–1482. 16. Sidorov N.A. Differential Equations with the Volterra Operator under Derivative// Mathematics.Izvestiya Vuzov, 1 (1984). 17. Sidorov N.A. On some Class of Singular Differential Equations with Convergence// Mat.Zametki 35 (1984), —p.569–578; English transl. in Math. Notes 35 (1984). 18. Sidorov N.A. A-adjoint Sets of Linear Operators and their Applications to the Differential Equations// In: ”Methods of optimization and operations research”, Irkutsk, SEI, 1984 — p.169–185. 19. Sviridyuk G.A. On the General Theory of Semigroup of Operators// Uspekhi Mat. Nauk. 49 (1994) —p.47–74. 20. Loginov B.V. Branching theory of solutions of nonlinear equations at conditions of a group invariance. — Tashkent, ”Fan”, 1985. 21. Trenogin V.A., Sidorov N.A., Loginov B.V.// Differ. and Integral Equations — Ohio, USA, 1990, v.3, no.1, p.145–154. 22. Trenogin V.A., Sidorov N.A., Loginov B.V. Potentiality, Group Symmetry and Bifurcation in the Theory of Branching Equation // Differ. and Integral Equations, Volume 3, Number 1, 1990. —p.145–154. 23. Vainberg M.M., Trenogin V.A. The Theory of Branching of Solutions of Nonlinear Equations. — ”Nauka”, Moscow, 1969; English trans., Wolters-Noordhoff, Groningen, 1974. 24. Zavalishin S.T., Sesekin A.N. Impulse Processes, Models and Applications. — ”Nauka”, Moscow, 1992.