ORDINARY DIFFERENTIAL EQUATIONS

1. 12 years teaching experience at Sambalpur University
2. 25 years research experience

Post Graduate Level

:

Real Analysis, Ordinary Differential Equations, Functional Analysis, Optimization Techniques, Complex Analysis, Mathematical Methods, Functional Differential Equations

1. Oscillation Theory for Differential equations, Difference equations, Hyers-Ulam Stability for ODE and Difference equations.

Ph.D. Candidates	:	06 (04 awarded)
M.Tech./M.Phil. Candidates	:	22

1. 1) Life member of ‘Indian Mathematical Society’ # T- 09- 054 .
2. 2) Life member of ‘The Indian Science Congress Association’ # L36774.

International Publications

1. A. K. Tripathy, G. N. Chhatria; Oscillation criteria for first order neutral impulsive difference equations with constant coefficients, Differ. Equ. Dyn. Syst., 31(2023), 209-222.
2. 85. A. K. Tripathy, S. Das; Necessary and sufficient conditions for oscillation of nonlinear neutral difference systems of dim-2, Nonauton. Dyn. Syst., 9(2022), 91-102.
3. 84. R. R. Mohanta, A. K. Tripathy; Unbounded Oscillation Criteria for Fourth Order Neutral Differential Equations of Non-canonical Type, Mathematica Slovaca, 72(2022), 661-676.
4. 83. A. K. Tripathy, S. S. Santra; Necessary and sufficient conditions for oscillation of a class of second order impulsive systems, Differ. Equ. Dyn. Syst., 30(2022), 433-450.
5. 82. A. K. Tripathy, G. N. Chhatria; On the behavior of solutions of neutral impulsive difference equations of second order, Math. Commun. 25(2020), 297-314.
6. 81. A. K. Tripathy, G. N. Chhatria; Nonlinear oscillation and second order impulsive neutral difference equations, Filomat, 35 (2021), 3365-3381.
7. 80. A. K. Tripathy, R. R. Mohanta; Unbounded Oscillation of Fourth Order Functional Differential Equations, Mathematica Slovaca, 70(2020), 1153-1164.
8. 79. A. K. Tripathy, R. R. Mohanta; On Oscillatory Fourth Order Nonlinear Neutral Differential Equations-IV, Mathematica Slovaca 69 (2019), 1099-1116.
9. 78. A. K. Tripathy, R. R. Mohanta; On Oscillatory Fourth Order Nonlinear Neutral Differential Equations-III, Mathematica Slovaca 68 (2018), 1385-1396.
10. 76. E. Schmeidel, A. K. Tripathy; Oscillation criteria for three dimensional linear difference systems, Appl. Anal. Dis. Math., 12(2018), 347-361.
11. 75. A. K. Tripathy, B. Panda; Oscillation of nonlinear fourth order mixed neutral differential equations, Math. Slovaca, 66(2016), 853-838.
12. 74. A. K. Tripathy; Oscillation criteria for a class of first order neutral impulsive differential-difference equations, J. Appl. Anal. Comp. 4(2014), 89-101.
13. 73. A. K. Tripathy, S. Panigrahy, K. Srilakshmi; Generalized Emden- Fowler-neutral type equations with Properties A & B, Dyn. Syst. Appl. 23(2014), 1-14.
14. 72. A. K. Tripathy, Oscillation criteria for a class of nonlinear fourth order neutral differential equation, Mathematica Slovaca, 63(2013), pp. 243-262.
15. 71. A. K. Tripathy, Oscillation criteria for a class of nonlinear fourth order neutral differential equation, Mathematica Slovaca, 63(2013), pp. 243-262.
16. 70. A.K.Tripathy, S.Panigrahi & R. Basu; Oscillation results for fourth order nonlinear mixed neutral differential equations-II, Nonlinear Oscillation,15(2012), pp. 539-555.
17. 69. A. K. Tripathy, S. Panigrahi, On the oscillation of a class of nonlinear delay difference equations of second order, Ind.J.Pure & Appl. Math. 42(2011), 27-40..
18. 68. A. K. Tripathy, Oscillation and nonoscillation of a class of nonlinear second order mixed difference equations, Elec . J. Qualit.Theory of Diff. Equ, (2010).
19. 67. A. K. Tripathy, Some oscillation results for second order nonlinear dynamic equations of neutral type, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), e1727 – e1735.
20. 66. A. K. Tripathy, Oscillation criteria for first-order systems of linear difference equations, Elect. J. Diff. Eqn. Vol. 2009 (2009), No. 29, 1 – 11.
21. 65. A. K. Tripathy, Oscillation of Fourth Order Nonlinear Neutral Difference Equations-II, Mathematica Slovaca, 58 (2008), 581 – 604.
22. 64. A. K. Tripathy, On the Oscillation of a Second Order Nonlinear Neutral Delay Difference Equations, Elec. J. Qualit. Theory of Diff.Equ, 11 (2008), 1 – 12.
23. 63. A. K. Tripathy, Oscillation of Fourth Order Nonlinear Neutral Difference Equations-I, Mathematica Slovaca, 58 (2008), 1 – 20.
24. 62. N. Parhi and A. K. Tripathy, On Oscillatory Fourth Order Nonlinear Neutral Differential Equations-II, Mathematica Slovaca 55 (2005), 183 – 202.
25. 61. N. Parhi and A. K. Tripathy, On Oscillatory Fourth Order Nonlinear Neutral Differential Equations-I, Mathematica Slovaca 54 (2004), 369 - 388.
26. 60. N. Parhi and A. K. Tripathy, Oscillation of a Class of Nonlinear Neutral Difference Equations of Higher Order, J. Math. Anal. Appl. 284 (2003), 756 – 774.
27. 59. N. Parhi and A. K. Tripathy, Oscillation of Forced Nonlinear Neutral Delay Difference Equations of First Order, Czec.Math.J.53 (2003), 83 – 101.
28. 58.N. Parhi and A. K. Tripathy, Oscillation Criteria for Forced Nonlinear Neutral Delay Difference Equations of First Order, Diff.Eqns.Dyne.Sys.8 (2000), 81 – 97.
29. 57. A. K. Tripathy; Existence of periodic solutions of second order nonlinear neutral differential equations, Functional Diff. Equs., 28(2021), 159-170.
30. 56. A. K. Tripathy, S. S. Santra; Necessary and sufficient conditions for oscillation of second order differential equations with nonpositive neutral coefficients, Math. Bohe., 146(2021), 185-197.
31. 55. A. K. Tripathy; On positive periodic solutions of a class of first order neutral differential equations, Glob. J. Pure and Appl. Math. , 16(2020), 811-818.
32. 54. A. K. Tripathy, S. S. Santra; On oscillatory second order nonlinear impulsive systems of neutral type, Stud. Univ. Babes-Bolyai Math. 65(2020), 503-519.
33. 53. A. K. Tripathy, G. N. Chhatria; On oscillatory first order neutral impulsive difference equations, Math. Bohemica, 145 (2020), 361-375.
34. 52. A. K. Tripathy, G. N. Chhatria; Nonlinear second order impulsive difference equations and their oscillation properties Tatra Mt. Math. Publ., 76(2020), 171-190.
35. 51.A. K. Tripathy; Oscillation of unbounded solutions of fourth order neutral dynamic equations via Taylor’s formula, Func. Diff. Equ. , 27(2020), 15-28.
36. 50. A. K. Tripathy; On Unbounded oscillation of fourth order functional difference equations, Diff. Equ. Appl., 3(2020), 259-275.
37. 49. A. K. Tripathy, S. S. Santra; Necessary and sufficient conditions for oscillations to a second order neutral differential equation with impulses, Kragujevac J. Math. 47(2023), 81-93.
38. 48. A. K. Tripathy, G. N. Chhatria; Oscillation of second order nonlinear impulsive differential equations with nonpositive neutral coefficients, J. Nonlin. Model. Anal., 2(2020), 525-540.
39. 47. A. K. Tripathy, G. N. Chhatria; On the behavior of solutions of neutral impulsive difference equations of second order, Math. Commun. 25(2020), 297-314.
40. 46. A. K. Tripathy, S. S. Santra; On oscillatory nonlinear forced neutral impulsive systems of second order, Nonlinear Oscillation 23(2020), 274-288.
41. 45. N. Parhi, A. K. Tripathy; Characterization of higher-order neutral difference equations with several delays, Inter. J. Diff. Equs., 14(2019), 127-148.
42. 44. A. K. Tripathy, G. N. Chhatria; Oscillation of second order nonlinear impulsive neutral differential equations, Int. J. Appl. Compu. Math. 5(2019), 1-12.
43. 43. S. S. Santra, A. K. Tripathy; On oscillatory first order nonlinear neutral differential equations with nonlinear impulse, J. Appl. Math. Compu. 59(2019), 257-270.
44. 42. A. K. Tripathy, G. N. Chhatria; Oscillation Criteria for forced first order nonlinear neutral impulsive difference system, Tatra Mountain Math. Publ. 71(2018), 175-193.
45. 41. A. K. Tripathy, A. K. Sethi; Sufficient conditions for oscillation and nonoscillation of a class of second order neutral differential equations, Adv. Dyn. Syst. Appl., 13(2018), 73-90.
46. 40. S. S. Santra, A. K. Tripathy; Oscillation of unforced impulsive neutral delay differential equations of first order, Commu. Appl. Anal., 22(2018), 567-582.
47. 39. A. K. Tripathy; Oscillation of a class of neutral delay dynamic equations of fourth order, Glo. Stoch. Anal., 5(2018), 15-29.
48. 38. A. K. Tripathy, P. Senapati: Hyers-Ulam stability of first order linear difference operators on Banach space, J. Adv. Math. 14(2018), 1-11.
49. 37. A. K. Sethi, A. K. Tripathy; Oscillation of sublinear second order neutral differential equations via Riccati transformation, Springer Proceedings in Mathematics & Statistics 230(2018), 543-557.
50. 36. A. K. Tripathy; New oscillation criteria for a class of second order neutral delay dynamic equations, DCDIS: Series A- Mathematical Analysis, 25(2018), 141-157.
51. 35. A. K. Tripathy; On oscillatory nonlinear fourth order difference equations with delays, Mathematica Bohemica, 1(2018), 25-40.
52. 34. A. K. Tripathy; Hyers-Ulam stability of second order linear difference equations, Int. J. Diff. Appl., 1(2017), 53-65.
53. 33. A. K. Sethi, A. K. Tripathy; Riccati transformation and oscillation of superlinear second order functional differential equations, Proceeding DSTA-2017, Mathematical and Numerical Aspects of Dynamical System Analysis, 479-490.
54. 32. A. K. Tripathy, S. S. Santra: Characterization of a class of second order neutral impulsive systems via pulsatile constant, Diff. Equ. Appl., 9(2017), 87-98.
55. 31. A. K. Tripathy, A. K. Sethi; Oscillation of sublinear and superlinear second order neutral differential equations, IJPAM, 113(2017), 73-91.
56. 30. A. K. Tripathy, S. S. Santra, S. Pinelas; Necessary and sufficient conditions for asymptotic behavior of solutions of a class of first-order impulsive systems, Adv. Dyn. Sys. Appl. 11(2016), 135-145.
57. 29. A. K. Tripathy, S. S. Santra: Pulsatile constant and characterization of first order neutral impulsive differential equations, Commu. Appl. Anal., 20(2016), 65-76.
58. 28. A. K. Tripathy; New oscillation criteria for fourth order neutral dynamic equations, Commu. Appl. Anal., 20(2016), 13-24.
59. 27. A. K. Tripathy, B. Panda; On oscillatory fourth-order non-linear neutral differential equations, Int. J. Dyn. Sys. Diff. Equ., 6(2016), 147-160.
60. 26. A. K. Tripathy, B. Panda, A. K. Sethi; On oscillatory nonlinear second order neutral delay differential equations, Differ. Equ. Appl. 8(2016), 247-258.
61. 25. A. K. Tripathy, S. S. Santra; Oscillation properties of a class of second order impulsive differential systems of neutral type, Functional Diff. Equ., 23(2016), 57-71.
62. 24. A. K. Tripathy, S. S. Santra; Necessary and sufficient conditions for oscillation of a class of first order impulsive differential equations, Functional Diff. Equ., 22(2015), 149-167.
63. 23. A. K. Tripathy, R. R. Mohanta; Oscillation properties of a class of second order neutral differential equations with piecewise constant arguments, Rom. J. Math. Comp. Sci. 5(2015), 178-190.
64. 22. A. K. Tripathy, A. Satapathy; Hyers-Ulam stability of fourth order Euler’s differential equations, J. Compu. Sci. Appl. Math., 1(2015), 49-58.
65. 21. A. K. Tripathy, S. Panigrahi, P. R. Reddy; Oscillation of nonlinear fourth order mixed neutral dynamic equations, Functional Diff. Equ., 21(2015), 69-91.
66. 20. A. K. Tripathy, S. Panigrahi, P. R. Reddy; Oscillation of a class of fourth order functional dynamic equations, Functional Diff. Equ., 21(2014), 91-108.
67. 19. A. K. Tripathy, S. Panigrahi, R. Basu; Oscillatory and asymptotic behavior of fourth order nonlinear neutral delay differential equations with positive and negative coefficients, Nr 52(2014), 155-174.
68. 18. A. K. Tripathy, A. Satapathy; Hyers-Ulam stability of third order Euler’s differential equations, J. Nonlinear Dyn. 2014(2014), 1-6.
69. 17. A. K. Tripathy; New oscillation criteria for fourth order difference equations, Adv. Dyn. Syst. Appl. 8(2013), 387-399.
70. 16. A.K.Tripathy; Oscillatory behavior of a class of nonlinear fourth order functional difference equations Inter.J.Difference Equ., 7(2012), pp. 79-97.
71. 15. A.K.Tripathy; Riccati transformation and sublinear oscillation for second order neutral delay dynamic equations, J.Appl.Math.& Informatics, 30(2012),pp.1005-1021.
72. 14. A. K. Tripathy; Oscillation theorems for fourth order nonlinear neutral equations with quasi-derivatives-I, Int. J. Math. Sci. Appl. 1(2011), pp.377-393.
73. 13. A. K. Tripathy, K. V. V. Seshagiri Rao, Oscillation properties of a class of nonlinear differential equations of neutral type, Fasciculi Mathematici, Nr 48(2012),pp.129-144.
74. 12. A.K.Tripathy; Asymptotic integration of higher order nonlinear neutral dynamic equations, Far East J. Appl. Math., 51 (2011), 27-44.
75. 11. A. K. Tripathy, S. Panigrahi, Oscillation in nonlinear neutral difference equations with positive and negative coefficients, Inter. J.Difference Equations, Vol 5, Issue2 (2010), 251-265.
76. 10. A. K. Tripathy, Oscillation properties of a class of neutral differential equations positive and negative coefficients, Fasciculi Mathematici Nr 45(2010), 133-155.
77. 9. A. K. Tripathy, Oscillatory behavior of a class of nonlinear system of first difference equations, Inter.J.Difference Eqns., Vol 5, Issue 1(2010), 113-127.
78. 8. A. K. Tripathy, Oscillation of a class of fourth order nonlinear mixed neutral difference equations Inter. J. Difference Equations, Vol 4, Issue 2 (2009).
79. 7. A. K. Tripathy, Oscillation of a Class of Superlinear Neutral Difference Equations of Higher Order, Inter.J.Scint.Comp. (2007), 69 – 80.
80. 6. N. Parhi and A. K. Tripathy, Oscillation of a Class of Neutral Difference Equations of First Order, J.Difference Equations Appl.9 (2003), 933 – 946.
81. 5. N. Parhi and A. K. Tripathy, Oscillation of a Class of Forced Nonlinear Neutral Difference Equations of Higher Order, “Proceedings of the VIII Ramanujan Symposium on Recent Developments in Nonlinear Systems”, 2002.
82. 4. N. Parhi and A. K. Tripathy, On Third Order Difference Equations, J.Difference Equations.Appl.8 (2002), 415 – 426.
83. 3. N. Parhi and A. K. Tripathy, On Asymptotic Behaviour and Oscillation of Forced First Order Nonlinear Neutral Difference Equations, Fasciculi Mathematici, Nr 32 (2001), 83 – 95.
84. 2. N. Parhi and A. K. Tripathy, On Oscillatory Third Order Difference Equations, J.Difference Equations.Appl.6 (2000), 53 – 74.
85. 1. N. Parhi and A. K. Tripathy, Oscillatory Behaviour of Second Order Difference Equations, Commu.Appl.Nonlin.Anal.6 (1999), 79 – 100.

International Conferences

1. 12th Colloquium on the Qualitative Theory of Differential Equations, University of Szeged, Szeged, Hungary, June 19–23, 2023.
2. International Conference on Differential and Difference Equations & Applications, June 5-9, 2017, Military Academy, Amadora, Lisbon, Portugal.
3. 10th International Conference on Progress on Difference Equations, May 17-20, 2016, University of Latvia, Riga, Latvia.
4. International Conference on Differential Equations, Difference Equations and Special Functions, September 3-7, 2012, University of Patras, Patras, Greece.
5. World Congress of Nonlinear Analysts, July 02-09, 2008, Organized by Florida Institute of Technology, Florida, USA.
6. Fourth International Conference on Dynamic Systems and Applications, May 21-24, 2003 Morehouse College, Georgia, Atlanta, U. S. A.

1. Hyers-Ulam Stability of Ordinary Differential Equations, CRC Press, Taylor & Francis Group, 2021. ISBN # 978-0-367-63668-5.

Present Address :  Dr. A. K. Tripathy Associate Professor Dept. of Mathematics Sambalpur University Sambalpur-768019, ODISHA

Permanent Address :  Dr. Arun Kumar Tripathy At / P.O. Chikili , Via – Khallikote Dist – Ganjam , Pin – 761030 (ODISHA)