Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
functional differential equation; periodic type boundary value problem; solvability; unique solvability
functional differential equation; periodic type boundary value problem; solvability; unique solvability
Summary:
Nonimprovable sufficient conditions for the solvability and unique solvability of the problem \[ u^{\prime }(t)=F(u)(t)\,,\qquad u(a)-\lambda u(b)=h(u) \] are established, where $F:\rightarrow $ is a continuous operator satisfying the Carathèodory conditions, $h:\rightarrow R$ is a continuous functional, and $\lambda \in $.
References:
[1] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F.: Introduction to the theory of functional differential equations. Nauka, Moscow, 1991 (In Russian). MR 1144998 | Zbl 0725.34071
[2] Azbelev, N V., Rakhmatullina L. F.: Theory of linear abstract functional differential equations and applications. Mem. Differential Equations Math. Phys. 8 (1996), 1–102. MR 1432626 | Zbl 0870.34067
[3] Bernfeld S. R., Lakshmikantham V.: An introduction to nonlinear boundary value problems. Academic Press, Inc., New York and London, 1974. MR 0445048 | Zbl 0286.34018
[4] Bravyi E.: A note on the Fredholm property of boundary value problems for linear functional differential equations. Mem. Differential Equations Math. Phys. 20 (2000), 133–135. MR 1789344 | Zbl 0968.34049
[5] Bravyi E., Hakl R., Lomtatidze A.: Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. Czechoslovak Math. J. 52 (2002), No. 3, 513–530. MR 1923257 | Zbl 1023.34055
[6] Bravyi E., Hakl R., Lomtatidze A.: On Cauchy problem for the first order nonlinear functional differential equations of non–Volterra’s type. Czechoslovak Math. J. 52 (2002), No. 4, 673–690. MR 1940049
[7] Bravyi E., Lomtatidze A., Půža B.: A note on the theorem on differential inequalities. Georgian Math. J. 7 (2000), No. 4, 627–631. MR 1811918 | Zbl 1009.34057
[8] Coddington E. A., Levinson N.: Theory of ordinary differential equations. Mc–Graw–Hill Book Company, Inc., New York–Toronto–London, 1955. MR 0069338 | Zbl 0064.33002
[9] Gelashvili S. M.: On a boundary value problem for systems of functional differential equations. Arch. Math. (Brno) 20 (1964), 157–168 (In Russian). MR 0784867
[10] Gelashvili S., Kiguradze I.: On multi-point boundary value problems for systems of functional differential and difference equations. Mem. Differential Equations Math. Phys. 5 (1995), 1–113. MR 1415806
[11] Hakl R.: On some boundary value problems for systems of linear functional differential equations. Electron. J. Qual. Theory Differ. Equ. (1999), No. 10, 1–16. MR 1711999 | Zbl 0948.34040
[12] Hakl R., Kiguradze I., Půža B.: Upper and lower solutions of boundary value problems for functional differential equations and theorems on functional differential inequalities. Georgian Math. J. 7 (2000), No. 3, 489–512. MR 1797786
[13] Hakl R., Lomtatidze A.: A note on the Cauchy problem for first order linear differential equations with a deviating argument. Arch. Math. (Brno) 38 (2002), No. 1, 61–71. MR 1899569 | Zbl 1087.34043
[14] Hakl R., Lomtatidze A., Půža B.: On nonnegative solutions of first order scalar functional differential equations. Mem. Differential Equations Math. Phys. 23 (2001), 51–84. MR 1873258 | Zbl 1009.34058
[15] Hakl R., Lomtatidze A., Půža B.: On a boundary value problem for first order scalar functional differential equations. Nonlinear Anal. 53 (2003), Nos. 3–4, 391–405. MR 1964333 | Zbl 1024.34056
[16] Hakl R., Lomtatidze A., Půža B.: New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. Math. Bohem. 127 (2002), No. 4, 509–524. MR 1942637 | Zbl 1017.34065
[17] Hakl R., Lomtatidze A., Šremr J.: On nonnegative solutions of a periodic type boundary value problems for first order scalar functional differential equations. Funct. Differ. Equ., to appear. MR 2095493
[18] Hakl R., Lomtatidze A., Šremr J.: On constant sign solutions of a periodic type boundary value problems for first order scalar functional differential equations. Mem. Differential Equations Math. Phys. 26 (2002), 65–90. MR 1929099
[19] Hale J.: Theory of functional differential equations. Springer–Verlag, New York–Heidelberg–Berlin, 1977. MR 0508721 | Zbl 0352.34001
[20] Hartman P.: Ordinary differential equations. John Wiley & Sons, Inc., New York–London–Sydney, 1964. MR 0171038 | Zbl 0125.32102
[21] Kiguradze I.: Some singular boundary value problems for ordinary differential equations. Tbilisi Univ. Press, Tbilisi, 1975 (In Russian). MR 0499402
[22] Kiguradze I.: Boundary value problems for systems of ordinary differential equations. Current problems in mathematics. Newest results, Vol. 30, 3–103, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vses. Inst. Nauchn. i Tekh. Inform., Moscow (1987) (In Russian). MR 0925829 | Zbl 0782.34025
[23] Kiguradze I.: Initial and boundary value problems for systems of ordinary differential equations I. Metsniereba, Tbilisi, 1997 (In Russian). MR 1484729
[24] Kiguradze I., Půža B.: On boundary value problems for systems of linear functional differential equations. Czechoslovak Math. J. 47 (1997), No. 2, 341–373. MR 1452425 | Zbl 0930.34047
[25] Kiguradze I., Půža B.: Conti–Opial type theorems for systems of functional differential equations. Differ. Uravn. 33 (1997), No. 2, 185–194 (In Russian). MR 1609904
[26] Kiguradze I., Půža B.: On boundary value problems for functional differential equations. Mem. Differential Equations Math. Phys. 12 (1997), 106–113. MR 1636865 | Zbl 0909.34054
[27] Kiguradze I., Půža B.: On the solvability of nonlinear boundary value problems for functional differential equations. Georgian Math. J. 5 (1998), No. 3, 251–262. MR 1618364 | Zbl 0909.34057
[28] Kolmanovskii V., Myshkis A.: Introduction to the theory and applications of functional differential equations. Kluwer Academic Publishers 1999. MR 1680144 | Zbl 0917.34001
[29] Schwabik Š., Tvrdý M., Vejvoda O.: Differential and integral equations: boundary value problems and adjoints. Academia, Praha 1979. MR 0542283 | Zbl 0417.45001
[30] Tsitskishvili R. A.: Unique solvability and correctness of a linear boundary value problem for functional–differential equations. Rep. Enlarged Sessions Sem. I. N. Vekua Inst. Appl. Math. 5 (1990), No. 3, 195–198 (In Russian).
Search
Partner of
