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

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1. 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
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. (1996) Zbl0870.34067MR1432626
3. Bernfeld S. R., Lakshmikantham V., An introduction to nonlinear boundary value problems, Academic Press, Inc., New York and London, 1974. (1974) Zbl0286.34018MR0445048
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. Zbl0968.34049MR1789344
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. Zbl1023.34055MR1923257
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. MR1940049
7. 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
8. Coddington E. A., Levinson N., Theory of ordinary differential equations, Mc–Graw–Hill Book Company, Inc., New York–Toronto–London, 1955. (1955) Zbl0064.33002MR0069338
9. 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
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. (1995) MR1415806
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. (1999) Zbl0948.34040MR1711999
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. MR1797786
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. Zbl1087.34043MR1899569
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. Zbl1009.34058MR1873258
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. Zbl1024.34056MR1964333
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. Zbl1017.34065MR1942637
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. MR2095493
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. MR1929099
19. Hale J., Theory of functional differential equations, Springer–Verlag, New York–Heidelberg–Berlin, 1977. (1977) Zbl0352.34001MR0508721
20. Hartman P., Ordinary differential equations, John Wiley & Sons, Inc., New York–London–Sydney, 1964. (1964) Zbl0125.32102MR0171038
21. Kiguradze I., Some singular boundary value problems for ordinary differential equations, Tbilisi Univ. Press, Tbilisi, 1975 (In Russian). (1975) MR0499402
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). (1987) Zbl0782.34025MR0925829
23. Kiguradze I., Initial and boundary value problems for systems of ordinary differential equations I, Metsniereba, Tbilisi, 1997 (In Russian). (1997) MR1484729
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. (1997) Zbl0930.34047MR1452425
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). (1997) MR1609904
26. Kiguradze I., Půža B., On boundary value problems for functional differential equations, Mem. Differential Equations Math. Phys. 12 (1997), 106–113. (1997) Zbl0909.34054MR1636865
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. (1998) Zbl0909.34057MR1618364
28. Kolmanovskii V., Myshkis A., Introduction to the theory and applications of functional differential equations, Kluwer Academic Publishers 1999. (1999) Zbl0917.34001MR1680144
29. Schwabik Š., Tvrdý M., Vejvoda O., Differential and integral equations: boundary value problems and adjoints, Academia, Praha 1979. (1979) Zbl0417.45001MR0542283
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). (1990)