# Solvability of a periodic type boundary value problem for first order scalar functional differential equations

Robert Hakl; Alexander Lomtatidze; Jiří Šremr

Archivum Mathematicum (2004)

- Volume: 040, Issue: 1, page 89-109
- ISSN: 0044-8753

## Access Full Article

top## Abstract

top## How to cite

topHakl, Robert, Lomtatidze, Alexander, and Šremr, Jiří. "Solvability of a periodic type boundary value problem for first order scalar functional differential equations." Archivum Mathematicum 040.1 (2004): 89-109. <http://eudml.org/doc/249311>.

@article{Hakl2004,

abstract = {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 $.},

author = {Hakl, Robert, Lomtatidze, Alexander, Šremr, Jiří},

journal = {Archivum Mathematicum},

keywords = {functional differential equation; periodic type boundary value problem; solvability; unique solvability; unique solvability},

language = {eng},

number = {1},

pages = {89-109},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Solvability of a periodic type boundary value problem for first order scalar functional differential equations},

url = {http://eudml.org/doc/249311},

volume = {040},

year = {2004},

}

TY - JOUR

AU - Hakl, Robert

AU - Lomtatidze, Alexander

AU - Šremr, Jiří

TI - Solvability of a periodic type boundary value problem for first order scalar functional differential equations

JO - Archivum Mathematicum

PY - 2004

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 040

IS - 1

SP - 89

EP - 109

AB - 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 $.

LA - eng

KW - functional differential equation; periodic type boundary value problem; solvability; unique solvability; unique solvability

UR - http://eudml.org/doc/249311

ER -

## References

top- Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Introduction to the theory of functional differential equations, Nauka, Moscow, 1991 (In Russian). (1991) Zbl0725.34071MR1144998
- Azbelev, N V., Rakhmatullina L. F., Theory of linear abstract functional differential equations and applications, Mem. Differential Equations Math. Phys. 8 (1996), 1–102. (1996) Zbl0870.34067MR1432626
- Bernfeld S. R., Lakshmikantham V., An introduction to nonlinear boundary value problems, Academic Press, Inc., New York and London, 1974. (1974) Zbl0286.34018MR0445048
- 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. Zbl0968.34049MR1789344
- 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. Zbl1023.34055MR1923257
- 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. MR1940049
- Bravyi E., Lomtatidze A., Půža B., A note on the theorem on differential inequalities, Georgian Math. J. 7 (2000), No. 4, 627–631. Zbl1009.34057MR1811918
- Coddington E. A., Levinson N., Theory of ordinary differential equations, Mc–Graw–Hill Book Company, Inc., New York–Toronto–London, 1955. (1955) Zbl0064.33002MR0069338
- Gelashvili S. M., On a boundary value problem for systems of functional differential equations, Arch. Math. (Brno) 20 (1964), 157–168 (In Russian). (1964) MR0784867
- 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. (1995) MR1415806
- 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. (1999) Zbl0948.34040MR1711999
- 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. MR1797786
- 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. Zbl1087.34043MR1899569
- 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. Zbl1009.34058MR1873258
- 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. Zbl1024.34056MR1964333
- 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. Zbl1017.34065MR1942637
- 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. MR2095493
- 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. MR1929099
- Hale J., Theory of functional differential equations, Springer–Verlag, New York–Heidelberg–Berlin, 1977. (1977) Zbl0352.34001MR0508721
- Hartman P., Ordinary differential equations, John Wiley & Sons, Inc., New York–London–Sydney, 1964. (1964) Zbl0125.32102MR0171038
- Kiguradze I., Some singular boundary value problems for ordinary differential equations, Tbilisi Univ. Press, Tbilisi, 1975 (In Russian). (1975) MR0499402
- 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). (1987) Zbl0782.34025MR0925829
- Kiguradze I., Initial and boundary value problems for systems of ordinary differential equations I, Metsniereba, Tbilisi, 1997 (In Russian). (1997) MR1484729
- Kiguradze I., Půža B., On boundary value problems for systems of linear functional differential equations, Czechoslovak Math. J. 47 (1997), No. 2, 341–373. (1997) Zbl0930.34047MR1452425
- Kiguradze I., Půža B., Conti–Opial type theorems for systems of functional differential equations, Differ. Uravn. 33 (1997), No. 2, 185–194 (In Russian). (1997) MR1609904
- Kiguradze I., Půža B., On boundary value problems for functional differential equations, Mem. Differential Equations Math. Phys. 12 (1997), 106–113. (1997) Zbl0909.34054MR1636865
- 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. (1998) Zbl0909.34057MR1618364
- Kolmanovskii V., Myshkis A., Introduction to the theory and applications of functional differential equations, Kluwer Academic Publishers 1999. (1999) Zbl0917.34001MR1680144
- Schwabik Š., Tvrdý M., Vejvoda O., Differential and integral equations: boundary value problems and adjoints, Academia, Praha 1979. (1979) Zbl0417.45001MR0542283
- 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). (1990)

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.