Author

# Ravi P. Agarwal

Other affiliations: Bohai University, King Fahd University of Petroleum and Minerals, Shandong Normal University, King Saud University, National University of Ireland, University of Florence, University of Manitoba, Florida Institute of Technology, Texas A&M University–Kingsville, National University of Ireland, Galway, National Technical University of Athens, Changchun University, King Abdulaziz University, National University of Singapore

Bio: Ravi P. Agarwal is a academic researcher from Texas A&M University. The author has contributed to research in topic(s): Boundary value problem & Differential equation. The author has an hindex of 79, co-authored 1595 publication(s) receiving 34854 citation(s). Previous affiliations of Ravi P. Agarwal include Bohai University & King Fahd University of Petroleum and Minerals.

Topics: Boundary value problem, Differential equation, Nonlinear system, Fixed-point theorem, Fixed point

##### Papers

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04 Nov 2019-

Abstract: Preliminaries linear initial value problems miscellaneous difference equations difference inequalities qualitative properties of solutions of difference systems qualitative properties of solutions of higher order difference equations qualitative properties of solutions of neutral difference equations boundary value problems for linear systems boundary value problems for nonlinear systems miscellaneous properties of solutions of higher order linear difference equations boundary value problems for higher order difference equations Sturm-Liouville problems and related inequalities difference inequalities in several independent variables.

922 citations

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Abstract: In this survey paper, we shall establish sufficient conditions for the existence and uniqueness of solutions for various classes of initial and boundary value problem for fractional differential equations and inclusions involving the Caputo fractional derivative. The both cases of convex and nonconvex valued right hand side are considered. The topological structure of the set of solutions is also considered.

693 citations

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31 Dec 1998-

Abstract: Preface. Ordinary Differential Equations. 1. First Order Initial Value Problems. 2. Second Order Initial Value Problems. 3. Positone Boundary Value Problems. 4. Semi-positone Boundary Value Problems. 5. Semi-Infinite Interval Problems. 6. Mixed Boundary Value Problems. 7. Singular Boundary Value Problems. 8. General Singular and Nonsingular Boundary Value Problems. 9. Quasilinear Boundary Value Problems. 10. Delay Boundary Value Problems. 11. Coupled System of Boundary Value Problems. 12. Higher Order Sturm-Liouville Boundary Value Problems. 13. (n,p) Boundary Value Problems. 14. Focal Boundary Value Problems. 15. General Focal Boundary Value Problems. 16. Conjugate Boundary Value Problems. Difference Equations. 17. Discrete Second Order Boundary Value Problems. 18. Discrete Higher Order Sturm-Liouville Boundary Value Problems. 19. Discrete (n,p) Boundary Value Problems. 20. Discrete Focal Boundary Value Problems. 21. Discrete Conjugate Boundary Value Problems. Integral and Integrodifferential Equations. 22. Volterra Integral Equations. 23. Hammerstein Integral Equations. 24. First Order Integrodifferential Equations. References. Authors Index. Subject Index.

626 citations

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Abstract: We present some fixed point results for monotone operators in a metric space endowed with a partial order using a weak generalized contraction-type assumption.

542 citations

##### Cited by

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[...]

TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

30,199 citations

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Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

3,015 citations

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TL;DR: It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related and converse Lyap Unov results can only assure the existence of continuous Lyap unov functions.

Abstract: Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.

3,009 citations

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01 Jan 2015-

2,819 citations