List of Selected Publications of G.Jaiani

LIST OF SELECTED PUBLICATIONS OF

GEORGE JAIANI

(Other transcriptions: Dzhaiani, Dzaiani)

1. On the Deflections of Thin Wedge-shaped Shells, Bulletin of the Academy of Science of the Georgian SSR, Vol. 65, 3, pp. 543-546, 1972 (in Russian, Georgian and English summaries)

2. On One Problem of an Elastic Wedge-shaped Body, Bulletin of the Academy of Science of the Georgian SSR, Vol. 70, 3, pp. 557-560, 1973 (in Russian, Georgian and English summaries)

3. On One Problem for the Fourth Order Degenerate Equation, Bulletin of the Academy of Science of the Georgian SSR, Vol. 75, 1, pp. 17-20, 1974 (in Russian, Georgian and English summaries)

4. On a Wedge-shaped Body Arbitrary Loaded Along the Cusped Edge, Bulletin of the Academy of Science of the Georgian SSR, Vol.75, 2, pp. 309-312, 1974 (in Russian, Georgian and English summaries)

5. Arbitrary Loaded Elastic Half-plane Whose Young's Modulus is Power Function of Depth, Materials of the I All-union School in Theory and Numerical Methods in Shell and Plate Theory, Tbilisi University Press, pp. 351-361, 1975 (in Russian)

6. On a Wedge-shaped Shell, Proceedings of X All-union Conference in Shell and Plate Theory, Tbilisi: "Metsniereba", pp. 94-101, 1975 (in Russian),

7. Riquier Problems with Weight for a Fourth Order Degenerate Equation, Dokl., Akad. Nauk SSSR, Tom 231, 6, pp. 1285-1288, 1976 (in Russian), Riquier Problems with Weight for a Certain Degenerate Equation of Fourth Order, Soviet Math. Dokl., Vol.17, 6, pp. 1715- 1719, 1976

8. A Generalization of the Poisson Formula in Case of a Half-plane for a Degenerate Equation of Even Order, Dokl. Akad.Nauk SSSR, Tom 235, N 6, pp. 1245-1248, 1977 (in Russian), A Generalization of the Half-plane Poisson Formula for a Degenerate Equation of Even Order, Soviet Math.Dokl.Vol.18, 4, pp.1132-1135, 1977

9. Bending of a Plate with Power Law Changing Stiffness, Annuaire Des Ecoles Superieures Mechanique Technique, Vol.XII, 2, pp.15-19, 1977 (in Russian)

10. The Riquier Problem for a Degenerate Equation, Complex Analysis and its Applications, Papers Dedicated to I.Vekua‘s 70-th Anniversary, Moscow: Nauka Press, pp. 209-216, 1978 (in Russian)

11. On Some Boundary Value Problems for Prismatic Cusped Shells, in Theory of Shells, Koiter W.T. and Mikhailov G.K., Eds., North-Holland Pub.Comp., pp. 339-343, 1980

12. On a Physical Interpretation of Fichera's Function, Acad.Naz.dei Lincei, Rend.della Sc.Fis.Mat.e Nat., S. VIII, Vol.LXVIII, fasc.5, pp. 426-435, 1980

13. The Problem V for the Euler-Poisson-Darboux Equation, Reports of Seminar of I.Vekua Institute of Applied Mathematics, Vol.15, pp.77-83, 1981 (in Russian)

14. Solution of some Problems for a Degenerate Elliptic Equation of Higher Order and their Applications to Prismatic Shells, Tbilisi University Press, 1982 (in Russian, Georgian and English summaries)

15. Euler-Poisson-Darboux Equation, Tbilisi University Press, 1984 (in Russian, Georgian and English summaries)

16. Boundary Value Problems of Mathematical Theory of Prismatic Shells with Cusps, Proceedings of All-union Seminar in Theory and Numerical Methods in Shell and Plate Theory, Tbilisi University Press, pp.126-142, 1984 (in Russian)

17. Problems with Discontinuous Boundary Conditions for the Euler-Poisson-Darboux Equation, Reports of Seminar of I.Vekua Institute of Applied Mathematics, Vol.18, pp.74-77, 1984 (in Russian)

18. Approximate Solution of Boundary Value Problems in the Case of the Euler-Poisson-Darboux Equation, Reports of Seminar of I.Vekua Institute of Applied Mathematics, Vol.18, pp.78-82, 1984 (in Russian)

19. On the Behaviour of a Solution of the Vekua Problem for the Euler-Poisson-Darboux Equation in the Half-plane, Reports of Seminar of I.Vekua Institute of Applied Mathematics, Vol.19, pp.23-26, 1985 (in Russian)

20. Formulas of Schwarz Type for a Singular Differential Equation, Bulletin of the Academy of Sciences of the Georgian SSR, Vol.122, N 3, pp.469-472, 1986 (in Russian, Georgian and English summaries)

21. On the Influence of Coefficients of Junior Terms on Posing of Boundary Value Problems for Elliptic Equations with Order Degeneration, Reports of Enlarged Sessions of the Seminar of I.Vekua Institute of Applied Mathematics, Vol.2, N 1, pp.31-34, 1986 (in Russian)

22. The Weighted Dirichlet Problem with Discontinuous Boundary Data for the Euler-Poisson-Darboux Equation in a Half-Plane, Proceedings of I.Vekua Institute of Applied Mathematics, Vol.19, pp.38-59, 1987 (in Russian)

23. Weight Boundary Value Problems for a Linear Degenerate Elliptic Equation of Second Order, Uspekhi Matematichskikh Nauk, Vol.42, 4 (256), p.174, 1987 (in Russian)

24. Bending of Prismatic Cusped Shell With Power Law Changing Stiffness, Proceedings of the XIV All-union Conference in Shell and Plate theory, Tbilisi University Press, pp.474-479, 1987 (in Russian)

25. Linear Elliptic Equations with Order Degeneration and Prismatic Shells with Cusps, Proceedings of All-union Conference in Modern Problems of Mathematical Physics, Tbilisi University Press, Vol.1, pp.207-213, 1987 (in Russian)

26. The First Boundary Value Problem of Cusped Prismatic Shell Theory in Zero Approximation of Vekua Theory, Proceedings of I.Vekua Institute of Applied Mathematics, Vol.29, pp.5-38, 1988 (in Russian, Georgian and English summaries)

27. On the Problem of Behaviour of Solutions of Boundary Value Problems in the Neighbourhood of Discontinuity Points of Boundary Data, Reports of Enlarged Sessions of the Seminar of I.Vekua Institute of Applied Mathematics, Vol.4, 1, pp.34-37, 1989

28. On a Way of Construction of Solutions of Boundary Value Problems for Higher Order Equations, Rendiconti di Matematica, Serie VII, Vol.10, pp.717-731, 1990

29. The Generalized Holmgren Problem for the Equation yDu+bu_y=0 in the Case of a Half-circle, Reports of Enlarged Session of the Seminar of I.Vekua Institute of Applied Mathematics of Tbilisi State University, Vol.6, 1, pp.21-24, 1991

30. On Some Applications of Variational Methods in the Theory of Bending of Prismatic Cusped Shells, Proceedings of I.Vekua Institute of Applied Mathematics of Tbilisi State University, Vol.47, pp.36-44, 1992

31. An Example of Non-unique Solvability of Fichera Problem in the Classical Sense, Reports of Enlarged Session of the Seminar of I.Vekua Institute of Applied Mathematics of Tbilisi State University, Vol.8, 1, pp.31-34,1993

32. On a Way of Solution of BVPs for a Class of Third Order Partial Differential Equations, Reports of Enlarged Session of the Seminar of I.Vekua Institute of Applied Mathematics of Tbilisi State University, Vol.10, 1, pp. 32-35, 1995

33. On a Generalization of the Keldysh Theorem, Georgian Mathematical Journal, Vol.2, 3, pp.291-297, 1995

34. Elastic Bodies with Non-smooth Boundaries – Cusped Plates and Shells, Zeitschrift fuer Angewandte Mathematik und Mechanik, Vol.76, Supplement 2, pp.117-120, 1996

35. The Main Boundary Value Problems of Bending of Cusped Plate in Weighted Sobolev Spaces, Applied Mathematics and Informatics, Vol. 1, No.1, pp. 78-84, 1996

36. On a Modification of the Lax-Milgram Theorem, Reports of Enlarged Session of the Seminar of I.Vekua Institute of Applied Mathematics of Tbilisi State University , Vol.12, 1, pp.5-8, 1997

37. On Boundary Value Problems for Conjugate Generalized Harmonic Functions, Ricerche di Matematica, Vol. 47, fasc. 2, pp. 231-256, 1998

38. On a Model of a Bar with Variable Thickness, BULLETIN of TICMI, Vol.2, pp.36-40, 1998 (for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)

39. On a Cylindrical Bending of a Prismatic Shell with Two Cusped Edges Under Action of an Idial Fluid, BULLETIN of TICMI, Vol.2, pp.30-34, 1998 (coauthor N. Chinchaladze, for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)

40. Bending of an Orthotropic Cusped Plate, Appl. Math. Inform., Vol. 4, No. 1, pp. 29-65, 1999

41. Initial and Boundary Value Problems for Singular Differential Equations and Applications to the Theory of Cusped Bars and Plates, Complex methods for partial differential equations (ISAAC Serials, Vol. 6), Eds.: H. Begehr, O. Celebi, W. Tutschke. Kluwer, Dordrecht, pp.113-149, 1999

42. Oscillation of an Orthotropic Cusped Plate, Reports of Enlarged Session of the Seminar of I.Vekua Institute of Applied Mathematics of Tbilisi State University, Vol. 14, N 1, pp. 24-31, 1999

43. On a Vibration of an Elastic Cusped Bar, BULLETIN of TICMI, Vol.4, pp. 24-28, 2000 (coauthor S.Kharibegashvili, for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)

44. The First Boundary Value Problem for the System of Cusped Prismatic Shells in the First Approximation, Appl. Math. Inform., Vol.5, No. 2, pp. 26-46, 2000 (with: G. Devdariani, S. Kharibegashvili, D. Natroshvili)

45. On a Mathematical Model of Bars with Variable Rectangular Cross-sections, ZAMM-Zeitschrift fuer Angewandte Mathematik und Mechanik, Vol.81, 3, pp.147-173, 2001

46. Application of Vekua's Dimension Reduction Method to Cusped Plates and Bars, Bull. TICMI (Tbilisi International Centre of Mathematics and Informatics), Vol.5, pp. 27-34, 2001 (for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)

47. Dynamical Problems in the (0,0) and (1,0) Approximations of a Mathematical Model of Bars. In "Functional-Analytic and complex Methods, Interactions, and Applications to PDEs". Proceedings of the International Graz Workshop, Graz, Austria, 12-16 February 2001, World Scientific, pp.188-248, 2001 (with S.S. Kharibegashvili)

48. On a Cusped Elastic Solid-Fluid Interaction Problem, Appl. Math. Inform, Vol. 6, No 2, pp. 25-64, 2001 (Coauthor N. Chinchaladze)

49. Static and Dynamical Problems for a Cusped Beam, Proceedings of I.Vekua Institute of Applied Mathematics of Tbilisi State University, Vol. 52, pp. 1-36, 2002

50. Theory of Cusped Euler-Bernoulli Beams and Kirchoff-Love Plates, Lecture Notes of TICMI, vol.3, 2002 (for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)

51. Relation of Hierarchical Models of Cusped Elastic Plates and Beams to the Three-dimensional Models, Reports of the Seminar of I.Vekua Institute of Applied Mathematics, 28, 31-39, 2002

52. Hierarchical Models for Elastic Cusped Plates and Beams, Lecture Notes of TICMI, vol.4, 2003 (with: S. Kharibegashvili, D. Natroshvili, W.L. Wendland, for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)

53. Bending of a Cusped Plates on an Elastic Foundation, Bulletin of TICMI, Vol. 8, pp. 22-31, 2004 (for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)

54. Mathematical Models of Mechanics of Continua, Tbilisi University Press, Tbilisi, 2004 (Textbook in Georgian)

55. Two-dimensional Hierarchical Models for Prismatic Shells with Thickness Vanishing at the Boundary, Journal of Elasticity, Vol. 77, No. 2, 95-122, 2004 (with: S. Kharibegashvili, D. Natroshvili, W.L. Wendland)

56. On Big Deflections of Cusped Plates, Bulletin of TICMI, Vol. 9, 6-13, 2005 (with: N. Chinchaladze)

57. Oscillation of Cusped Euler-Bernoulli Beams and Kirchhoff-Love Plates, Hacettepe Journal of Mathematics and Statistics, Vol. 35 (1), 7-53, 2006 (with: A. Kufner)

58. A Cusped Prismatic Shell-like Body under the Action of Concentrated Moments, ZAMP-Zeitschrift fuer Angewandte Mathematik und Physik (DOI 10.1007/s 00033-006-6005-7, Online First, published online: 20 November, 2006, access: http://www.birkhauser.ch)

59. A cusped Prismatic Shell-like Body with the Angular Projection under the Action of a Concentrated Force, Rendiconti Academia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni, 124⁰(2006), Vol. XXX, facs. 1, 65-82, 65-82

60. Some Degenerate Elliptic Systems and Applications to Cusped Plates, Mathematische Nachrichten, 280, 4, 388-407, 2007 (with B.-Wolfgang Schulze)

61. On Physical and Mathematical Moments and the Setting of Boundary Conditions for Cusped Prismatic Shells and Beams, Proceedings of the IUTAM Symposium on Relation of Shell, plate, Beam, and 3D Models Dedicated to Centenary of Ilia Vekua, 23-27 April, 2007, Tbilisi, Georgia. IUTAM Bookseries, Vol. 9, 133-146, Editors G. Jaiani, P. Podio-Guidugli. Springer, 2008

62. On a Nonlocal Boundary Value problem for a System of Singular Differential Equations, Applicable Analysis: An International Journal, Volume 87, No. 1, 83 – 97, 2008; First published electronically on 19 December 2007, (DOI: 10.1080/00036810701729964, access: http://www.tandf.co.uk/journals/titles/00036811.asp)

63. Existence and Uniqueness Theorems for Cusped Prismatic Shells in the N-th Hierarchical Model, Mathematical Methods in Applied Sciences, Vol. 31, No. 11, 1345-1367, 2008 (with N. Chinchaladze, R. Gilbert, G. Jaiani, S. Kharibegashvili, D. Natroshvili, DOI 10.1002/mma.975, access for electronic version: http://www3.interscience.wiley.com/search/allsearch?mode=viewselected&product=journal&ID=117905390& view_selected.x=111&view_selected.y=7, Published Online: 4 Feb 2008)

64. Cylindrical Bending of a Cusped Plate with Big Deflections, Journal of Mathematical Sciences, Volume 157, Number 1, 52-69, Springer, 2009, [Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 51, Differential Equations and Their Applications, 2008] (with N. Chinchaladze) access: http://www.springerlink.com/content/bt22900q5v238682/?p=1af5abb4d88148f9b5c7775b1319afab&pi=2