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.
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