List of Publications

Monographs:
  1. A. Lomtatidze, S. Mughigulashvili, Some two-poit boundary value problems for second order functional differential equations, Folia Facul. Sci. Natur. Univ. Masar. Brun., Mathematica 8, Brno: Masaryk University, 2000, 72 pages.
  2. R. Hakl, A. Lomtatidze, J. Šremr, Some boundary value problems for first order scalar functional differential equations, Folia Facul. Sci. Natur. Univ. Masar. Brun., Mathematica 10, Brno: Masaryk University, 2002, 300 pages.
    Reprint
  3. R. Hakl, A. Lomtatidze, I. P. Stavroulakis, Bounded solutions to the first-order scalar finctional differential equations, Mem. Differential Equations Math. Phys. 59 (2013), 1-104.
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Articles:
  1. A. Lomtatidze, On a boundary value problem for second order linear differential equations with nonintegrable singularities, Proc. I. Vekua Inst. Appl. Math. 14 (1983), 136-144, in Russian.
  2. A. Lomtatidze, I. Kiguradze, On certain boundary value problems for second order ordinary differential equations with singularities, J. Math. Anal. Appl. 101 (1984), No. 2, 325-347.
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  3. A. Lomtatidze, On a singular boundary value problem for second order linear differential equations, Boundary Value Problems, Perm (1984), 46-50.
  4. A. Lomtatidze, On solvability of boundary value problems for second order nonlinear differential equations with singularities, Rep. of enlarged session of the seminar of I. Vekua Inst. Appl. Math. 1985, Vol. 1 (1985), No. 3, 85-92, in Russian.
  5. A. Lomtatidze, On oscillatory properties of solutions of second order linear differential equations, Seminar of I. Vekua Inst. Appl. Math. Reports. 19 (1985), 39-53, in Russian.
  6. A. Lomtatidze, On a singular three-point boundary value problem, Proc. I. Vekua Inst. Appl. Math. 17 (1986), 122-133, in Russian.
  7. A. Lomtatidze, On a boubdary value problem for second order nonlinear ordinary differential equations with singularities, Differ. Uravn. 22 (1986), No. 3, 416-426, in Russian.
  8. A. Lomtatidze, On positive solutions of singular boundary value problems for second order nonlinear ordinary differential equations, Differ. Uravn. 22 (1986), No. 6, 1092, in Russian.
  9. A. Lomtatidze, N. Kandelaki, On the approximate solution of a certain evolution equation, Comp. Math. and Programming 27 (1987), No. 1, 85-90, in Russian.
  10. A. Lomtatidze, On positive solutions of boundary value problems for second order ordinary differential equations with singularities, Differ. Uravn. 23 (1987), No. 10, 1685-1692, in Russian.
  11. A. Lomtatidze, Concerning solvability of singular boundary value problems for second order ordinary differential equations, Proc. I. Vekua Inst. Appl. Math. 22 (1987), 135-149, in Russian.
  12. A. Lomtatidze, On some boundary value problems for two-dimensional differential systems, Rep. of enlarged session of the seminar of I.Vekua Inst. Appl. Math. 1992, Vol. 7 (1992), No. 3, 68-70.
  13. A. Lomtatidze, On some two-poit boundary value problems for two-dimensional systems of ordinary differential equations, Georgian Math. J. 1 (1994), No. 3, 303-314.
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  14. A. Lomtatidze, Existence of conjugate points for second order linear differential equations, Georgian Math. J. 2 (1995), No. 1, 93-98.
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  15. A. Lomtatidze, Nonlocal boundary value problem for second order linear ordinary differential equations, Differ. Uravn. 31 (1995), No. 3, 446-455, in Russian.
  16. A. Lomtatidze, On a nonlocal boundary value problem for second order linear ordinary differential equations, J. Math. Anal. Appl. 193 (1995), No. 2, 889-908.
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  17. A. Lomtatidze, N. Partsvania, On oscillatory properties of second order systems of ordinary differential equations, Mem. Differential Equations Math. Phys. 5 (1995), 122-124.
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  18. A. Lomtatidze, S. Mughigulashvili, On periodic solutions of second order functional differential equations, Mem. Differential Equations Math. Phys. 5 (1995), 125-126.
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  19. A. Lomtatidze, On oscillation of third order linear differential equation, Differ. Uravn. 32 (1996), No. 10, 1348-1354, in Russian.
  20. A. Lomtatidze, Oscillation and nonoscillation of Emden-Fowler type equation of second order, Arch. Math. (Brno) 32 (1996), No. 3, 181-193.
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  21. A. Lomtatidze, Oscillation and nonoscillation criteria for second order linear differential equation, Georgian Math. J. 4 (1997), No. 2, 129-138.
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  22. A. Lomtatidze, N. Partsvania, Oscillation and nonoscillation criteria for two-dimensional system of first order linear ordinary differential equations, Georgian Math. J. 6 (1999), No. 3, 285-298.
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  23. A. Lomtatidze, T. Chantladze, N. Kandelaki, Oscillation and nonoscillation criteria for a second order linear equations, Georgian Math. J. 6 (1999), No. 5, 401-414.
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  24. A. Lomtatidze, T. Chantladze, N. Kandelaki, On zeros of solutions of a second order singular half-linear equation, Mem. Differential Equations Math. Phys. 7 (1999), 127-158.
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  25. O. Došlý, A. Lomtatidze, Disconjugacy and disfocality criteria for second order singular half-linear differential equations, Ann. Polon. Math. 72 (1999), No. 3, 273-284.
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  26. A. Lomtatidze, N. Kandelaki, D. Ugulava, On oscillation and nonoscillation of second order half-linear equations, Georgian Math. J. 7 (2000), No. 2, 329-346.
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  27. A. Lomtatidze, L. Malaguti, On a nonlocal boundary value problem for second order singular equations, Georgian Math. J. 7 (2000), No. 2, 133-157.
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  28. A. Lomtatidze, N. Kandelaki, T. Chantladze, The p-Laplacian and connected pairs of functions, Mem. Differential Equations Math. Phys. 20 (2000), 113-126.
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  29. A. Lomtatidze, E. Bravyi, B. Půža, A note on the theorem on differential inequalities, Georgian Math. J. 7 (2000), No. 4, 627-631.
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  30. A. Lomtatidze, T. Chantladze, D. Ugulava, Conjugacy and disconjugacy criteria fir second order linear ordinary deifferential equations, Arch. Math. (Brno) 36 (2000), No. 4, 313-323.
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  31. A. Lomtatidze, T. Chantladze, N. Kandelaki, On quadratically integrable solutions of the second order linear equation, Arch. Math. (Brno) 37 (2001), No. 1, 57-62.
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  32. R. Hakl, A. Lomtatidze, B. Půža, On nonnegative solutions of first order scalar functional differential equations, Mem. Differential Equations Math. Phys. 23 (2001), 51-84.
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  33. R. Hakl, A. Lomtatidze, B. Půža, On periodic solutions of first order nonlinear functional differential equations of non-Volterra's type, Mem. Differential Equations Math. Phys. 24 (2001), 83-105.
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  34. A. Lomtatidze, L. Adamec, Oscillation criteria for third order linear equations, Differ. Uravn. 37 (2001), No. 6, 723-729, in Russian.
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  35. R. Hakl, A. Lomtatidze, B. Půža, On periodic solutions of first order linear functional differential equations, Nonlin. Anal. 49 (2002), 929-945.
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  36. R. Hakl, A. Lomtatidze, 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.
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  37. R. Hakl, A. Lomtatidze, J. Šremr, On an antiperiodic type boundary value problem for first order linear functional differential equations, Arch. Math. (Brno) 38 (2002), No. 2, 149-160.
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  38. R. Hakl, A. Lomtatidze, J. Šremr, On a periodic type boundary value problem for first order nonlinear functional differential equations, Nonlin. Anal. 51 (2002), 425-447.
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  39. R. Hakl, A. Lomtatidze, J. Šremr, On constant sign solutions of a periodic type boundary value problems for first order scalar functional differential equations, Mem. Differential Equat. Math. Phys 26 (2002), 65-90.
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  40. R. Hakl, A. Lomtatidze, J. Šremr, Solvability and unique solvability of a periodic type boundary value problems for first order scalar functional differential equations, Georgian Math. J. 9 (2002), No. 3, 525-547.
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  41. A. Lomtatidze, T. Chantladze, N. Kandelaki, D. Ugulava, On a generalization of the Dirichlet integral, Georgian Math. J. 9 (2002), No. 3, 449-459.
  42. R. Hakl, E. Bravyi, A. Lomtatidze, Optimal conditions on unique solvability of the Cauchy problem for the first order linear functional differential equations, Czechoslovak Math. J. 52 (2002), No. 3, 513-530.
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  43. R. Hakl, E. Bravyi, A. Lomtatidze, On Cauchy problem for the first order nonlinear functional differential equations, Czechoslovak Math. J. 52 (2002), No. 4, 673-690.
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  44. R. Hakl, A. Lomtatidze, J. Šremr, On a periodic type boundary value problem for first order linear functional differential equations, Neliniini Koliv. 5 (2002), No. 3, 416-432.
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  45. R. Hakl, A. Lomtatidze, B. Půža, New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations, Math. Bohemica 127 (2002), No. 4, 509-524.
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  46. A. Lomtatidze, P. Torres, On a two-point boundary value problem for second order singular equations, Czechoslovak Math. J. 53 (2003), No. 1, 19-43.
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  47. A. Lomtatidze, L. Malaguti, On a two-point boundary value problem for second order ordinary differential equations with singularities, Nonlin. Anal. 52 (2003), No. 6, 1553-1567.
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  48. R. Hakl, A. Lomtatidze, B. Půža, On a boundary value problem for first order scalar functional differential equations, Nonlin. Anal. 53 (2003), No. 3-4, 391-405.
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  49. R. Hakl, A. Lomtatidze, J. Šremr, On an antiperiodic type boundary-value problem for first order nonlinear functional differential equations of non-Volterra's type, Neliniini Koliv. 6 (2003), No. 4, 550-573.
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  50. R. Hakl, A. Lomtatidze, B. Půža, On a periodic boundary value problem for the first order scalar functional differential equation, Differ. Uravn. 39 (2003), No. 3, 320-327, in Russian.
    Reprint
  51. R. Hakl, A. Lomtatidze, I. P. Stavroulakis, On a boundary value problem for scalar functional differential equations, Abstr. Appl. Anal. 2004 (2004), No. 1, 45-67.
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  52. R. Hakl, A. Lomtatidze, J. Šremr, On nonnegative solutions of a periodic type boundary value problem for first order scalar functional differential equations, Funct. Differ. Equ. 11 (2004), No. 3-4, 363-394.
  53. A. Lomtatidze, Z. Opluštil, On nonnegative solutions of a certain boundary value problem for first order linear functional differential equations, Electron. J. Qual. Theory Differ. Equ., Proc. 7th Coll. QTDE (2004), No. 16, 1-21.
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  54. R. Hakl, A. Lomtatidze, J. Šremr, Solvability of a periodic type boundary value problem for first order scalar functional differential equations, Arch. Math. (Brno) 40 (2004), No. 1, 89-109.
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  55. A. Lomtatidze, P. Vodstrčil, On nonnegative solutions of second order linear functional differential equations, Mem. Differential Equations Math. Phys. 32 (2004), 59-88.
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  56. A. Lomtatidze, P. Vodstrčil, On sign constant solutions of certain boundary value problems for second-order functional differential equations, Appl. Anal. 84 (2005), No. 2, 197-209.
  57. A. Lomtatidze, H. Štěpánková, On sign constant and monotone solutions of second order linear functional differential equations, Mem. Differential Equations Math. Phys. 35 (2005), 65-90.
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  58. O. Došlý, A. Lomtatidze, Oscillation and nonoscillation criteria for half-linear second order differential equations, Hiroshima Math. J. 36 (2006), No. 2, 203-219.
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  59. A. Lomtatidze, P. Vodstrčil, On Solvability of a three-point boundary value problem for second order nonlinear functional differential equations, Mem. Differential Equations Math. Phys. 40 (2007), 55-65.
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  60. A. Lomtatidze, Z. Opluštil, J. Šremr, On a nonlocal boundary value problem for first order linear functional differential equations, Mem. Differential Equations Math. Phys. 41 (2007), 69-85.
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  61. A. Cabada, A. Lomtatidze, M. Tvrdý, Periodic problem involving quasilinear differential operator and weak singularity, Adv. Nonlinear Stud. 7 (2007), No. 4, 629-649.
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  62. A. Lomtatidze, S. Mukhigulashvili, J. Šremr, Nonnegative solutions of the characteristic initial value problem for linear partial functional-differential equations of hyperbolic type, Math. Comput. Modelling 47 (2008), No. 11-12, 1292-1313.
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  63. I. Kiguradze, A. Lomtatidze, On periodic solutions of linear differential equations with coefficients of alternating sign, Differ. Uravn. 44 (2008), No. 11, 1580-1581, in Russian.
  64. A. Lomtatidze, Z. Opluštil, J. Šremr, Solvability conditions for a nonlocal boundary value problem for linear functional differential equations, Fasc. Math. 41 (2009), 81-96.
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  65. A. Lomtatidze, Z. Opluštil, J. Šremr, Nonpositive solutions to a certain functional differential inequality, Nonlinear Oscil. 12 (2009), No. 4, 474-505.
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  66. I. Kiguradze, A. Lomtatidze, Periodic solutions of nonautonomous ordinary differential equations, Monatsh. Math. 159 (2010), No. 3, 235-252.
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  67. A. Domoshnitsky, A. Lomtatidze, A. Maghakyan, J. Šremr, Linear hyperbolic functional-differential equations with essentially bounded right-hand side, Abstr. Appl. Anal. 2011 (2011), ID 242965, 1-26.
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  68. A. Lomtatidze, J. Šremr, On Oscillation of second-order linear ordinary differential equations, Mem. Differential Equations Math. Phys. 54 (2011), 69-81.
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  69. A. Lomtatidze, J. Šremr, On the Cauchy problem for linear hyperbolic functional-differential equations, Czechoslovak Math. J. 62 (137) (2012), 391-440.
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  70. I. Kiguradze, A. Lomtatidze, N. Partsvania Some multi-point boundary value problems for second order singular differential equations, Mem. Differential Equations Math. Phys. 56 (2012), 133-141.
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  71. A. Lomtatidze, J. Šremr, On oscillation and nonoscillation of two-dimensional linear differential systems, Georgian Math. J. 20 (2013), No. 3, 573-600.
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  72. A. Lomtatidze, Z. Opluštil, Fredholm alternative for the second-order singular Dirichlet problem, Bound. Value Probl. 2014 (2014), No. 13, 1-15.
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  73. A. Lomtatidze, J. Šremr, Carathéodory solutions to a hyperbolic differential inequality with a non-positive coefficient and delayed arguments, Bound. Value Probl. 2014 (2014), No. 52, 1-13.
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  74. A. Lomtatidze, Z. Opluštil, Fredholm's third theorem for second-order singular Dirichlet problem, Bound. Value Probl. 2014 (2014), No. 59, 1-12.
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  75. M. Dosoudilová, A. Lomtatidze, J. Šremr, Oscillatory properties of solutions to certain two-dimensional systems of non-linear ordinary differential equations, Nonlin. Anal. 120 (2015), 57-75.
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Preprints:
  1. A. Lomtatidze, S. Mughigulashvili, J. Šremr Nonnegative solutions of the characteristic initial value problem for linear partial functional-differential equations of hyperbolic type, Mathematical Institute, Academy of Sciences of the Czech Republic, Preprint 160 (2005).
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To appear: