RAVI AGARWAL

Professor, Department of Mathematical Sciences
Ph.D., Indian Institute of Technology (Madras), India

PRINCIPLE RESEARCH INTERESTS

In the last century most of the sciences, engineering and technology have triggered a multitude of nonlinear complex phenomena. For the majority of these problems only nonnegative solutions make sense. These problems involve singular (with respect to dependent variable), or nonsingular second order ordinary or functional differential equations together with some boundary conditions over finite or infinite intervals. One of the fields in which our research continues is developing new theories for the existence of positive solutions of singular boundary value problems and applying the obtained results to diverse fields such as gas diffusion through porous media, thermal self-ignition of a chemically active mixture of gases in a vessel, catalytic theory, chemically reacting systems and adiabatic tubular reactors, diffusion of heat generated by positive temperature-dependent sources, fluid dynamics, electrical potential theory, combustion theory, steady-state of oxygen diffusion in a cell with Michaelis-Menten kinetics, cell membrane, and heat conduction in the human brain.

SELECTED PUBLICATIONS

    Research Monographs:

  • R.P. Agarwal, D. O'Regan and P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht (Holland), 1999, pp 417.

  • R.P. Agarwal, Difference Equations and Inequalities, Second Edition, Revised and Expanded, Marcel Dekker, New York, 2000, pp. 998.

  • R.P. Agarwal, D. O'Regan, Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht (Holland), 2001, pp 341.

  • R.P. Agarwal, M. Meehan and D. O'Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge, 2001, pp. 170.

  • R.P. Agarwal, S.R. Grace and D. O'Regan, Oscillation Theory for Second Order, Half-linear, Superlinear and Sublinear Dynamic Equations, Kluwer Academic Publishers, Dordrecht (Holland), 2002, pp 672.

  • R.P. Agarwal, S.R. Grace and D. O'Regan, Oscillation Theory for Second Order Dynamic Equations, Taylor & Francis, London, 2003, pp 404.

    • Research Papers:

  • R.P. Agarwal and D. O'Regan, Twin solutions to singular boundary value problems, Proceedings of the American Mathematical Society 128(2000), 2085-2094.

  • R.P. Agarwal and D. O'Regan, Existence theory for single and multiple solutions to singular positone boundary value problems, Journal of Differential Equations 175(2001), 393-414

  • R.P. Agarwal and D. O'Regan, Singular problems on the infinite interval modelling phenomena in draining flows, IMA Journal of Applied Mathematics 66 (2001), 621-635.

  • R.P. Agarwal and D. O'Regan, Infinite interval problems modelling the flow of a gas through a semi-infinite porous medium, Studies in Applied Mathematics 108 (2002), 245-257.

  • R.P. Agarwal and D. O'Regan, Existence criteria for singular boundary value problems with sign changing nonlinearities, Journal of Differential Equations 183 (2002), 409-433

  • R.P. Agarwal, D. O'Regan, V. Lakshmikantham and S. Leela, An upper and lower solution theory for singular Emden-Fowler equations, Nonlinear Analysis (Real World Applications) 3 (2002), 275-291.

Keywords

Differential equations
Difference equations
Fixed point theorems
Inequalities

Florida Institute of Technology
Department of Mathematical Sciences
150 West University Blvd.
Melbourne, FL 32901-6975
Fax (321) 674-7412
E-mail: agarwal@fit.edu