Publications

1. Set Valued functions in Frechet spaces: continuity, Hukuhara differentiability and applications to set differential equations, Non.Anal. TMA 61 (2005) 559-575. (with Galanis, G.N., Lakshmikantham, V., and Palamides, P. K.)

2. Nonuniform stability and boundedness criteria for set differential equations, Appl.Anal. 84 (2), 2005, 131-143 . ( with JV Devi)

3. Set Differential Systems and Vector Lyapunov functions, Appl.Math. Comp. 165 (2005), 539-548. (with JV Devi)

4. Stability criteria for set differential equations, Math.& Comp. Modelling. 41 (2005), 1371-1378.(with JV Devi)

5. Stability results for Set Difference Equations, Dyn. Sys. Appl. 13 (3&4). 2004, 479-485.(with M. Shaw)

6.Revisiting Fuzzy differential equations, Non.Anal.TMA 58 (2004), 351-358. (with V. Lakshmikantham and JV Devi).

7. Lyapunov Stability for Set Differential Equations. Dynamic Systems and Applications. 13(1), 2004, 1-10. (with V Lakshmikantham)

8. Generalized Proximal Normals and Flow Invariance for Differential Inclusions, Nonlinear Studies 10(1), 2003, 29-37. (with V. Lakshmikantham)

9. Set Differential equations and Flow Invariance, Applicable Analysis, 2003, 82(4), 357-368. (with V. Lakshmikantham)

10. Generalized proximal normals and Lyapunov Stability, Nonlinear Studies 10(4), 2003, 335-341. (with V. Lakshmikantham)

11. Generalized quasi-linearization method to semi-linear hyperbolic problems, Dis.Cont. Dyn.Sys.(DCDS) series A, 9(5), 2003, 1263-1275. (with Lakshmikantham and S. Koskal)

12. Comparison theorem for a nonlinear boundary value problem on time scales, J. Comp. and App. Math. (special issue on “Dynamic Equations on Time Scales”), 141, (1-2), 2002, 117-122.

13. Monotone iterative techniques for problems involving difference of two monotone functions, Appl. Math. & Comp. 133(1), 187-192, 2002. (MR2003f:34005) (with F.A. Mc Rae)

14. Trigonometric like operators in Banach spaces, Dynamic Systems and Appl. 10 (4), 2001, 551-562. (with S.G.Deo)

15. Generalized quasi-linearization for reaction-diffusion equation with periodic conditions, Prob. Nonlinear Analysis in Engineering Systems, 1 (13) 2001, 38-46. (with A.S.Vatsala)

16. Analyticity of semigroup generated by a class of differential operators with interface, Nonlinear Analysis, TMA 39 (2000) 779-791. (MR2000j:47075) (with Rajiv Kumar)

17. m-accretivity of the differential Operators with an interface, Nonlinear Analysis TMA , 24 (5), 1995, 765-772. (MR96b:34082) (with Rajiv Kumar)

18. Computation of Green’s matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators, Int. J. Math. and Math.Sci. 18 (4), 1995, 789-798(MR96d:34028) (with M Venkatesulu)

19. Singular selfadjoint Sturm-Liouville problems with interface, Far East Journal of Mathematical Sciences 1(1), 1993,103-116

20. Green’s matrices for a class of interface problems, Dynamic Systems and Applications, 2(1), 1993, 101-120 (MR93m:34038) (with M Venkatesulu)

21. Fundamental Systems and Solutions of non-homogeneous equations for a pair of mixed linear ordinary differential equations, J.Aust.Math.Soc.(Series A) 49, 1990, 161-173.(MR91b:34016) (with M Venkatesulu)

22. Selfadjoint boundary value problems associated with a pair of mixed linear ordinary differential equations, J. Math. Anal. Appl. 144 (2), 1989, 322-341(MR91b:47110) (with Venkatesulu)

23. Solutions of initial value problems associated with with a pair of mixed linear ordinary differential equations, J. Math. Anal. Appl. 148 (1), 1990 (MR91d:34006), 63-78 (with Venkatesulu)

Accepted for Publications


1. Generalized Flow Invariance for Differential Inclusions, To appear in JAMSA (with V. Lakshmikantham)

Publications in the proceedings of Conferences/Workshops


1. Trends in Wavelet methods for two point boundary value problems, to appear in the proceedings of the International conference on “Current trends in Differential Equations and Dynamical Systems,” Narosa Publishers.

2. Sobolov Spaces, in Topics in Sobolov spaces and applications, Proceedings of the workshop held at IIT, Kanpur, Dec, 1998, 44-59, Narosa Publishers.

3. Wavelet packets, Proceedings of the workshop on “Wavelet transform and applications” held at Madras Institute of Technology, Anna University, Chennai, Jan, 1997, 30-39.

4. Multiresolution approximations and Image compression, Proceedings of the Workshop “Wavelet transform and applications”, Madras Institute of Technology, Anna University. Chennai, Jan, 1997 , 40-50.

Research Report : A study of Wavelet Frames, Submitted to Department of Mathematics, IIT, Delhi, 1994.

Research Papers presented in conferences


1. Recent developments in the theory of Set Differential Equations, Fourth World Congress of Nonlinear Ananlysts-2004, Orlando, USA, 30 June- 7th July, 2004.

2. Proximal Aiming and Weak Invariance for Euler Solutions of Cauchy Problems, AMS Meeting, Univ. Central Florida, Orlando, 9-10, November, 2002.

3. Comparison theorem for lower and upper solutions of semi-linear hyperbolic problems, Third World Congress of Nonlinear Analysts- 2000, University of Catania, Catania, Italy, 19-26, July, 2000.

4. An existence theorem for two point boundary value problems on time scales, at the Year 2000-International Conference “Dynamic Systems and Differential Equations”, Kennesaw State University, Kennesaw,Georgia,USA,18-21, May, 2000

5. Generalized quasi-linearization for boundary value problems on time scales, Third international conference on “Nonlinear problems in aviation and Aerospace” at Embry-Riddle Aeronautical University, Daytona Beach, Florida, USA, 10-12, May, 2000

6. Adjoints of differential operators involving an interface, International Conference on “ Function spaces and applications to Partial Differential Equations” University of Delhi, Delhi, 15-19, 1997.

7. Regularization of Sturm Liouville operators an interface, International conference on “Differential equations, theory, methods and applications” BM Birla Science center, Hyderabad, 20-23,February, 1995.