List of Publications

List of Publications:

1. V. Chr. Covachev, Construction of a parametrix for a hyperbolic system with characteristics of variable multiplicity, Comptes rendus de l'Académie bulgare des Sciences, Tome 33 (1980), No. 10, 1313-1315. MR 82m:35148

2. Valery H. Covačev, Microlocal parametrix for the Cauchy problem for hyperbolic symmetric systems with symplectic multiple characteristics I, Serdica Bulgariae mathematicae publicationes, Vol. 8 (1982), No. 1, 64-81. MR 84k:35090

3. Valery H. Kovačev, Microlocal parametrix for the Cauchy problem for hyperbolic symmetric systems with symplectic multiple characteristics II, Serdica Bulgariae mathematicae publicationes, Vol. 8 (1982), No. 2, 204-213. MR 85d:35073

4. Kovachev V. Kh., Bilinear transformations of some differential equations with rational right-hand side, Vestn. Belarus State Univ., Ser. 1, Phys., Math. and Mech. (1983), No. 2, 45-47 (in Russian). MR 84k:34018

5. Kovachev V. Kh., On the birational transformations of differential equations with polynomial right-hand side, in: Proc. 6^th Conf. of Bulg. Postgrad. Students in USSR (1983), 603-607 (in Russian).

6. Kovachev V. Kh., Reduction of certain differential equations with rational right-hand side to “triangular” form by means of a bilinear transformation, Vestn. Belarus. State Univ., Ser. 1, Phys., Math. and Mech. (1984), No. 2, 61-62 (in Russian). MR 86c:34070

7. Kovachev V. Kh., On the triangulation of differential systems by means of a fractional-linear transformation, Ed. of J. “Izv. Vuzov. Math.”, Kazan', 1984, 48 p. The manuscript was deposed at VINITI (in Russian).

8. Kovachev V. Kh., Some bilinear invariants of two-dimensional autonomous systems of ordinary differential equations with rational right-hand side, Differential Equations, Vol. 21 (1985), No. 2, 331-334, 366 (in Russian). MR 86e:34074

9. Kovachev V. Kh., Invariants of bilinear transformations of differential systems, in: Differential Equations and Applications. Proceedings of the Third Conference, Roussé'85 (1987), 191-194 (in Russian). MR 88j:00018

10. Valery Kovachev, Smoothness of the billiard ball map for strictly convex domains near the boundary, Proceedings of the American Mathematical Society, Vol. 103 (1988), No. 3, 856-860. MR 89m:58121

11. V. C. Kovachev, G. S. Popov, Existence of invariant tori for the billiard ball map near an elliptic periodic geodesic, Comptes rendus de l'Académie bulgare des Sciences, Tome 41 (1988), No. 9, 19--22. MR 90d:58039

12. V. S. Georgiev, V. Ch. Kovachev, A weighted estimate of the solution to the wave equation, Comptes rendus de l'Académie bulgare des Sciences, Tome 42 (1989), No. 11, 17-20. MR 91i:35115

13. V. Chr. Kovachev, G. St. Popov, Invariant curves for the billiard ball map in the hyperbolic case, in: Applications of Mathematics in Engineering. Proceedings of the XV National Summer School. Varna'89 (1989), 211-214.

14. Valery Kovachev and Georgi Popov, Invariant tori for the billiard ball map, Transactions of the American Mathematical Society, Vol. 317 (1990), No. 1, 45-81. MR 90e:58050

15. V. Chr. Covachev, Billiard flow and the billiard ball map, in: First Colloquium on Differential Equations, Plovdiv, 1990, 7-10.

16. Kovachev Valeriy Khristov, Popov Georgiy Stefanov, Invariant sets of the billiard ball map and applications, in: Republican Scientific Lectures on Ordinary Differential Equations, Minsk, 1990, 62-63 (in Russian).

17. V. S. Georgiev and V. Chr. Kovachev, Nonlinear problems in quantum mechanics, Surveys on Analysis, Geometry and Mathematical Physics, Teubner-Texte zur Mathematik, Band 117 (1990), 54-137. MR 92j:35152

18. V. Chr. Covachev and V. S. Georgiev, Weighted decay estimate for the wave equation, Proceedings of the American Mathematical Society, Vol. 112 (1991), No. 2, 393-402. MR 91k:35143

19. V. Chr. Covachev, V. S. Georgiev, A counterpart of the Poincaré group for pseudodifferential operators, Comptes rendus de l'Académie bulgare des Sciences, Tome 44 (1991), No. 2, 17-20. MR 92j:58107

20. D. Bainov, V. Covachev, I. Stamova, Estimates of the solutions of impulsive quasilinear functional differential equations, Annales Faculté des Sciences de Toulouse, Vol. XII, No. 2 (1991), 149--161. MR 93j:34092

21. Valery Covachev, Global existence of small amplitude solutions of nonlinear hyperbolic equations via weighted estimates of Sobolev norms associated with a Lie group, in: Differential Equations. The Second Colloquium. Plovdiv, Bulgaria, 19-24 August 1991. World Scientific, Singapore - New Jersey - London - Hong Kong - Bangalore, 1992, 71-84. MR 93h:35123 (93g:34002 for the collection)

22. V. Covachev and V. Georgiev, A time-dependent Sobolev inequality related to a first-order pseudodifferential operator, in: Applications of Mathematics in Engineering. Proceedings of the XVII National Summer School. Varna'91 (1992), 99-102.

23. Valéry Covachev, Numerical-analytical method for finding periodic solutions of nonlinear impulsive singularly perturbed differential equations, in: Proceedings of the First International Colloquium on Numerical Analysis. Plovdiv, Bulgaria, 13-17 August 1992. VSP. Utrecht, The Netherlands, 1993, 39-50. (MR 97m:65010 for the collection)

24. Valéry Covachev, Initial value problem for a singularly perturbed nonlinear impulsive system in the critical case, in: Proceedings of the Third International Colloquium on Differential Equations. Plovdiv, Bulgaria, 18-22 August 1992. VSP. Utrecht, The Netherlands, 1993, 31-44. (MR 98a:00007 for the collection)

25. V. Covachev, Dirichlet problem for a second order quasilinear singularly perturbed impulsive differential equation, in: Selected Invited Lectures and Short Communications Delivered at the First International Colloquium on Numerical Analysis and the Third International Colloquium on Differential Equations (Plovdiv, 1992), 31-37.

26. V. Covachev, Almost periodic solutions of singularly perturbed linear systems of impulsive differential equations, in: Applications of Mathematics in Engineering. Proceedings of the XVIII National Summer School. Varna'92 (1993), 94-97.

27. Valéry Covachev, Periodic problem for singularly perturbed nonlinear impulsive systems and application to a model of metabolic system, in: Mathematical Population Dynamics 3 (Pau, France, 1992).

28. D. Bainov and V. Covachev, Impulsive Differential Equations with a Small Parameter, Series on Advances in Mathematics for Applied Sciences - Vol. 24, World Scientific Publishers, Singapore, New Jersey, London, Hong Kong, 1994, 268 p. MR 97i:34001

29. D. D. Bainov, V. Chr. Covachev, I. M. Stamova, Stability under persistent disturbances of impulsive differential-difference equations of neutral type, Journal of Mathematical Analysis and Applications, Vol. 187 (1994), No. 3, 790-808. MR 95j:34108

30. L. Jódar, R. J. Villanueva and V. Chr. Covachev, Periodic solutions of neutral impulsive systems with a small delay, in: Proceedings of the Fourth International Colloquium on Differential Equations. Plovdiv, Bulgaria, 18-23 August 1993. VSP. Utrecht, The Netherlands. Tokyo, Japan, 1994, 125-135.

(MR 98c:00012 for the collection)

31. L. Jódar, R. J. Villanueva, V. Chr. Covachev and J. M. Martín, Analytic-numerical solutions of variable coefficient second order delay differential equations, in: Proceedings of the Fourth International Colloquium on Differential Equations. Plovdiv, Bulgaria, 18-22 August 1993. VSP. Utrecht, The Netherlands. Tokyo, Japan, 1994, 137-146. (MR 98c:00012 for the collection)

32. L. Jódar, R. J. Villanueva and V. Chr. Covachev, Second order delay differential equations with variable coefficients: analytic-numerical solutions, in: 19-th Summer School “Applications of Mathematics in Engineering”, August 24-September 02, 1993. Varna, Bulgaria. Sofia, 1994, 99-113.

33. L. Jódar, R.J. Villanueva, V. Chr. Covachev, J. M. Martín, Analytic-numerical solutions of coupled variable coefficient second order delay differential equations, Differential Equations and Dynamical Systems.

34. D. D. Bainov and V. Chr. Covachev, Periodic solutions of impulsive systems with a small delay, J. Phys. A: Math. Gen. 27 (1994), 5551-5563. MR 95h:34103

35. D. D. Bainov and V. Chr. Covachev, Existence of periodic solutions of neutral impulsive systems with a small delay, in: 20-th Summer School “Applications of Mathematics in Engineering”. Varna, 26.08-02.09.1994. Sofia, 1995, 35-40.

36. D. D. Bainov and V. Chr. Covachev, Periodic solutions of impulsive systems with delay viewed as a small parameter, Rivista di Matematica Pura ed Applicata, 19 (1996), 9-25. MR 98j:34015

37. A. Boichuk, V. Covachev, Periodic solutions of impulsive systems with a small delay in the critical case of first order, in: Functional Differential-Difference Equations and Applications, Antalya, Turkey, 18-23 August 1997 (H. Akça, L. Berezansky, E. Braverman, L. Byszewski, S. Elaydi and I. Győri, eds.). Electronic Publishing House.

38. A. Boichuk, V. Covachev, Periodic solutions of impulsive systems with a small delay in the critical case of second order, Nonlinear Oscillations, 1 (1998), No. 1, 6-19.

39. Haydar Akça, Valéry Covachev, Periodic solutions of impulsive systems with delay, International Conference on Functional Differential Equations (Israel, 1998), Functional Differential Equations 5 (1998), No. 3-4, 275-286.

40. Alexander Boichuk, Valéry Covachev, Boundary value problems for impulsive systems with small concentrated delays, in: Applications of Mathematics in Engineering'24, eds. B. I. Cheshankov and M. D. Todorov, Heron Press, Sofia, 1999, pp. 59-62. MR 2000c:34169

41. V. C. Covachev, I. B. Risteski, Regular singularities in the simple reduction of the Poincaré differential equation to Cauchy matrix form, Comptes rendus de l'Académie bulgare des Sciences, Tome 52 (1999), No. 11-12, 21-24.

42. Ice Risteski, Kostadin Trenčevski and Valéry Covachev, A simple functional operator, New York Journal of Mathematics 5 (1999), 139-142.

43. J. Stefanovski, K. Trenčevski and V. Covachev, Cauchy problem and reduction of a system of partial differential equations, Tamkang J. of Mathematics 30, No. 4 (1999), 315-329.

44. Haydar Akça, Valéry Covachev, Periodic solutions of impulsive systems with periodic delays, Proceedings of the International Conference on Biomathematics Bioinformatics and Applications of Functional Differential - Difference Equations, Akdeniz University, July 14-19, 1999, pp. 65-76.

45. Kostadin G. Trenčevski, Ice B. Risteski and Valéry C. Covachev, On two complex functional equations of Fréchet's type, Proceedings of the International Conference on Biomathematics Bioinformatics and Applications of Functional Differential-Difference Equations, Akdeniz University, July 14-19, 1999, pp. 180-185.

46. Ice B. Risteski, Kostadin G. Trenčevski and Valéry C. Covachev, Reduction of the generalized Popov's differential equation to Birkhoff matrix form, Menemui Mat. 21 (1999), 59-69.

47. Valéry Covachev, Periodicity of the population size of an age-dependent model with a dominant age class by means of impulsive perturbations, Mathematical Population Dynamics 5 (Zakopane, Poland, 1998) Int. J. Appl. Math. And Comp. Sci. 10 (2000), No. 1, 147-155. MR 2001b:92021

48. V. Covachev, Bellman-Gronwall inequality, in: Encyclopaedia of Mathematics, Supplement II, ed. M. Hazewinkel, Kluwer Academic Publishers, Dordrecht, 2000, pp. 51-52.

49. Alexander Boichuk, Valéry Covachev, Weakly-nonlinear boundary value problems for impulsive systems with small concentrated delays of the argument, Nonlinear Oscillations, 3 (2000), No. 1, 13-30.

50. Jovan Stefanovski, Kostadin Trenčevski, Valéry Covachev, Charpit system of partial differential equations with algebraic constraints, J. Part. Diff. Equations 13 (2000), 151-162. MR 2001a:35039

51. Ice B. Risteski, Valéry Covachev, Multiple regular singularities of the Poincaré differential equation and its Cauchy matrix form, in: Application of Mathematics in Engineering and Economics'25, eds. B. I. Cheshankov and M. D.

Todorov, Heron Press, Sofia, 2000, pp. 66-69.

52. Ice B. Risteski, Kostadin Trenčevski and Valéry Covachev, On a linear vector functional equation, in: Some Problems of Applied Mathematics, eds. A. Ashyralyev and H. A. Yurtsever, Fatih University Publications, Istanbul, 2000, pp. 174-184.

53. Ice B. Risteski, Kostadin G. Trenčevski and Valéry C. Covachev, Reduction of the generalized Popov's differential equation to Birkhoff canonical matrix form, New Zealand J. of Mathematics 29 (2000), 61-69. MR 2001d:34012

54. Ice B. Risteski and Valéry C. Covachev, On some general classes of partial linear complex vector functional equations, SUT Journal of Mathematics 36 (2000), No. 2, 105-146.

55. I. B. Risteski, K. G. Trenčevski and V. C. Covachev, Cyclic complex vector functional equations, Applied Sciences, Vol. 2 (2000), No. 1, 13-18. MR 2001k:39037

56. Haydar Akça, Valéry Covachev, Periodic solutions of linear impulsive systems with periodic delays in the critical case, Third International Conference on Dynamic Systems & Applications, Atlanta, Georgia, May 1999, eds. G.S. Ladde, N. G. Medhin and M. Sambandham. Proceedings of Dynamic Systems and Applications, Vol. 3 (2001), pp. 15-22.

57. Ice B. Risteski, Kostadin G. Trenčevski, Valéry C. Covachev, A special Abel's integral equation, Missouri. J. Math. Sci. 13 (2001), No. 1, 53-64.

58. Ice B. Risteski, Kostadin G. Trenčevski, Valéry C. Covachev, An expanded class of parametric linear complex vector functional equations, Balkan J. Geom. Appl. 6 (2001), 63-86.

59. Ice B. Risteski, Kostadin G. Trenčevski, Valéry C. Covachev, Systems of Functional Equations, in: Applications of Mathematics in Engineering and Economics'26, eds. B. I. Cheshankov and M. D. Todorov, Heron Press, Sofia, 2001, pp. 113-118.

60. Ice B. Risteski, Kostadin G. Trenčevski and Valéry C. Covachev, Complex vector systems of partial functional equations, Analele Ştiinţifice ale Universităţii ``Al. I. Cuza'' din Iaşi, Tomul XLVII, s. I a, Matematică (2001), f. 2, 315-366.

61. Valéry Covachev, Haydar Akça and Fuat Yeniçerioğlu, Difference approximations for impulsive differential equations, Applied Mathematics and Computation 121 (2001), No. 2-3, 383-390.

62. Maria K. Koleva, Valéry C. Covachev, Common and different features between the behavior of the chaotic dynamical systems and the -type noise, Fluctuations and Noise Letters, Vol. 1 (2001), No. 2, R131-R149.

63. Haydar Akça & Valéry Covachev, Delay differential equations: mathematical modeling in medicine and periodic solutions of impulsive systems with periodic delays in the critical case, The Proceedings of Mathematics & Design 2001. The Third International Conference, Deakin University, Geelong, Australia, pp. 448-461.

64. Ice Risteski & Valéry Covachev, Complex Vector Functional Equations, World Scientific, New Jersey – London – Singapore – Hong Kong, 2001, 324 p. MR 2003c:39027

65. Haydar Akça, Abdelkader Boucherif, Valéry Covachev, Impulsive functional differential equations with nonlocal conditions, International Journal of Mathematics and Mathematical Sciences, Vol. 29 (2002), no. 5, 251-256.

66. Valéry Covachev, Almost periodic solutions of impulsive systems with periodic time-dependent perturbed delays, Functional Differential Equations, Vol. 9 (2002), No. 1-2, 91-108.

67. Valéry Covachev, Hasan Ali Yurtsever, Almost periodic solutions of impulsive systems with periodic fluctuations of the delay, in: Applications of Mathematics in Engineering and Economics'27, eds. B. I. Cheshankov and M. D. Todorov, Heron Press, Sofia, 2002, pp. 144-154.

68. Valéry Covachev, Zlatinka Covacheva, Haydar Akça, Eada Ahmed Al-Zahrani, Almost periodic solutions of neutral impulsive systems with periodic time-dependent perturbed delays, Central European Journal of Mathematics, 3 (2003), 292-314.

69. Haydar Akça, Rajai Alassar, Valéry Covachev and Zlatinka Covacheva, Discrete counterparts of continuous-time additive Hopfield-type neural networks with impulses, Dynamic Systems and Applications (to appear)

70. Ice B. Risteski, Kostadin G. Trenčevski, Valéry C. Covachev, On some simple complex vector functional equations, J. of the University of Braşov (to appear)

71. Ice B. Risteski, Kostadin G. Trenčevski and Valéry C. Covachev, On a class of parametric partial linear complex vector functional equations, Analele Universităţii din Craiova (to appear)

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