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Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

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Mathematica Slovaca

Abstract

General conditions for the unique solvability of a non-linear nonlocal boundary-value problem for systems of non-linear functional differential equations are obtained.

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References

  1. AZBELEV, N.— MAKSIMOV, V.— RAKHMATULLINA, L.: Introduction to the Theory of Linear Functional Differential Equations, World Federation Publishers Company, Atlanta, GA, 1995.

    MATH  Google Scholar 

  2. 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(127) (2002), 513–530.

    Article  MATH  MathSciNet  Google Scholar 

  3. DILNA, N.: On the unique solvability of the initial-value problem for non-linear functional-differential equations, Mem. Differential Equations Math. Phys. (To appear).

  4. DIL’NAYA, N. Z.— RONTO, A. N.: Some new conditions for the solvability of the Cauchy problem for systems of linear functional-differential equations, Ukrainian Math. J. 56 (2004), 1033–1053.

    MathSciNet  Google Scholar 

  5. DILNA, N. Z.— RONTO, A. N.: General conditions for the unique solvability of the initial-value problem for nonlinear functional-differential equations, Ukrainian Math. J. 60 (2008), No. 2, 167–172.

    MathSciNet  Google Scholar 

  6. DILNA, N. Z.— RONTO, A. N.: General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations, Math. Bohem. 133 (2008), 435–445.

    MATH  MathSciNet  Google Scholar 

  7. HAKL, R.— LOMTATIDZE, A.— PŮŽA, B.: On a boundary value problem for first-order scalar functional differential equations, Nonlinear Anal. 53 (2003), 391–405.

    Article  MATH  MathSciNet  Google Scholar 

  8. KRASNOSELSKII, M. A.: Positive Solutions of Operator Equations, Wolters-Noordhoff Scientific Publications Ltd., Groningen, 1964.

    Google Scholar 

  9. KRASNOSELSKII, M. A.— ZABREIKO, P. P.: Geometrical Methods of Nonlinear Analysis, Springer, Berlin-New York, 1984.

    Google Scholar 

  10. KRASNOSELSKII, M. A. — LIFSHITS, E. A. — POKORNYI, YU. V. — STETSENKO, V. YA.: Positively invertible linear operators and the solvability of nonlinear equations, Dokl. Akad. Nauk Tadzhik. SSR 17 (1974), 12–14.

    Google Scholar 

  11. LOMTATIDZE, A.— OPLUŠTIL, Z.: On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations, Electron. J. Qual. Theory Differ. Equ. 16 (2004), 1–21 (Proc. 7th Coll. Qualitative Theory of Differ. Equations).

    Google Scholar 

  12. LOMTATIDZE, A.— OPLUŠTIL, Z.— ŠREMR, J.: On a nonlocal boundary value problem for first order linear functional differential equations, Mem. Differential Equations Math. Phys. 41 (2007), 69–85.

    MATH  MathSciNet  Google Scholar 

  13. OPLUŠTIL, Z.: New solvability conditions for a nonlocal boundary-value problem for nonlinear functional differential equations, Nonlinear Oscil. 11 (2008), 384–406.

    Article  MathSciNet  Google Scholar 

  14. PYLYPENKO, V.— RONTO, A.— DILNA, N.: On the unique solvability of a non-local boundary value problem for linear functional differential equations, Math. Model. Anal. 13 (2008), 241–250.

    Article  MATH  MathSciNet  Google Scholar 

  15. ŠREMR, J.: On the Cauchy type problem for systems of functional differential equations, Nonlinear Anal. 67 (2007), 3240–3260.

    Article  MATH  MathSciNet  Google Scholar 

  16. ŠREMR, J.: Solvability conditions of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators, Math. Bohem. 132 (2007), 263–295.

    MATH  MathSciNet  Google Scholar 

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Author notes

  1. N. Dilna

    Present address: Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49 St., SK-814 73, Bratislava, Slovakia

Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3 St., 01601, Kiev, Ukraine

    N. Dilna

  2. Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, CZ-616 62, Brno, Czech Republic

    A. Ronto

Authors
  1. N. Dilna
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  2. A. Ronto
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Corresponding author

Correspondence to N. Dilna.

Additional information

Communicated by Michal Fečkan

The research was supported in part by the National Scholarship Program of the Slovak Republic, NAS of Ukraine, Grant No. 0108U004117, FRSF, Grant No. GP/F26/0154, AS CR, Institutional research plan AV0Z10190503, and GA CR, Grant No. 201/06/0254.

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Dilna, N., Ronto, A. Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations. Math. Slovaca 60, 327–338 (2010). https://doi.org/10.2478/s12175-010-0015-9

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  • DOI: https://doi.org/10.2478/s12175-010-0015-9

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