Faculty in the University of Dayton Department of Mathematics examine the art, science, application and philosophy of mathematics. Here, you can see a sampling of their research.

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Submissions from 2008

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Optimal selling rules in a regime-switching exponential Gaussian diffusion model, Paul W. Eloe, R. H. Liu, and Masako Yatsuki

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Qualitative Properties of Nonlinear Volterra Integral Equations, Muhammad Islam and Jeffrey T. Neugebauer

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An Order Model for Infinite Classical States, Joe Mashburn

Submissions from 2007

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A transform method in discrete fractional calculus, Ferhan M. Atici and Paul W. Eloe

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Fractional q-calculus on a time scale, Ferhan M. Atici and Paul W. Eloe

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Uniqueness implies existence and uniqueness conditions for nonlocal boundary value problems for nth order differential equations, Paul W. Eloe and Johnny Henderson

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Periodic Solutions of Neutral Nonlinear Systems of Differential Equations with Functional Delay, Muhammad Islam and Youssef Raffoul

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A Comparison of Three Topologies on Ordered Sets, Joe Mashburn

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A Spectral Order for Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn

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Forced Oscillations of a Class of Nonlinear Dispersive Wave Equations and their Stability, Muhammad Usman and Bingyu Zhang

Submissions from 2006

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A qualitative analysis on nonconstant graininess of the adaptive grids via time scales, Paul W. Eloe, Stefan Hilger, and Qin Sheng

Multiple solutions of a boundary value problem on an unbounded domain, Paul W. Eloe, Eric R. Kaufmann, and Christopher C. Tisdell

Submissions from 2005

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Positive operators and maximum principles for ordinary differential equations, Paul W. Eloe

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Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions, Paul W. Eloe and Bashir Ahmad

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Existence, uniqueness and constructive results for delay differential equations, Paul W. Eloe, Youssef N. Raffoul, and Christopher C. Tisdell

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Stability Properties of Linear Volterra Integrodifferential Equations with Nonlinear Perturbation, Muhammad Islam and Youssef Raffoul

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Boundedness and Stability in Nonlinear Delay Difference Equations Employing Fixed Point Theory, Muhammad Islam and Ernest Yankson

Submissions from 2004

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Maximum principles for a family of nonlocal boundary value problems, Paul W. Eloe

A note on quasilinearization for impulsive systems, Paul W. Eloe and S. G. Hristova

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Approximating crossed symmetric solutions of nonlinear dynamic equations via quasilinearization, Paul W. Eloe and Qin Sheng

Submissions from 2003

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Disconjugacy and Higher Order Dynamic Equations, Paul W. Eloe

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Sign properties of Green's functions for disconjugate dynamic equations on time scales, Paul W. Eloe

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The quasilinearization method on an unbounded domain, Paul W. Eloe

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Pair differentiation, Paul W. Eloe and Stefan Hilger

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A continuation of the discussion on cross symmetry of solutions, Paul W. Eloe and Qin Sheng

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Notes on crossed symmetry solutions of the two-point boundary value problems on time scales, Paul W. Eloe, Qin Sheng, and Johnny Henderson

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Exponential Stability in Nonlinear Difference Equations, Muhammad Islam and Youssef Raffoul

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Uniform Asymptotic Stability in Nonlinear Volterra Discrete Systems, Muhammad Islam, Youssef Raffoul, and Paul W. Eloe (0000-0002-6590-9931)

Submissions from 2002

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Generalized quasilinearization method for a second order three point boundary-value problem with nonlinear boundary conditions, Bashir Ahmad, Rahmat Ali Khan, and Paul W. Eloe

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The quasilinearization method for boundary value problems on time scales, Ferhan M. Atici, Paul W. Eloe, and Billur Kaymakçalan

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Upper and lower solution methods for fully nonlinear boundary value problems, Jeffrey Ehme, Paul W. Eloe, and Johnny Henderson

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The method of quasilinearization and dynamic equations on compact measure chains, Paul W. Eloe

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The method of quasilinearization and a three-point boundary value problem, Paul W. Eloe and Yang Gao

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Method of the quasilinearization for nonlinear impulsive differential equations with linear boundary conditions, Paul W. Eloe and S. G. Hristova

Submissions from 2001

On nonresonance impulsive functional differential equations with periodic boundary conditions, Mouffak Benchohra and Paul W. Eloe

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Existence of solutions for 2nth order nonlinear generalized Sturm-Liouville boundary value problems, Jeffrey Ehme, Paul W. Eloe, and Johnny Henderson

Monotone methods and fourth order Lidstone boundary value problems with impulse effects, Paul W. Eloe and Muhammad N. Islam

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Positive solutions of nonlinear functional difference equations, Paul W. Eloe, Y. Raffoul, D. T. Reid, and K. C. Yin

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The fast Fourier transform method and ill-conditioned matrices, Boon Yi Soon, Paul W. Eloe, and David Kammler

Submissions from 2000

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OIF Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, and Joe D. Mashburn

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Higher order dynamic equations on measure chains: Wronskians, disconjugacy, and interpolating families of functions, Martin Bohner and Paul W. Eloe

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Discrete Kiguradze type inequalities, John M. Davis and Paul W. Eloe

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Nonlinear eigenvalue problems for higher order Lidstone boundary value problems, Paul W. Eloe

A boundary value problem on an unbounded domain, Paul W. Eloe, Louis J. Grimm, and Joe D. Mashburn

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Countable positive solutions of a conjugate boundary value problem, Paul W. Eloe, Johnny Henderson, and Nickolai Kosmatov

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Extremal points for impulsive Lidstone boundary value problems, Paul W. Eloe, Johnny Henderson, and H. B. Thompson

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Comparison of Green's functions for a family of multipoint boundary value problems, Paul W. Eloe and Lingqin Zhang

Uniform Asymptotic Stability in Linear Volterra Integrodifferential Equations with Application to Delay Systems, Muhammad Islam, Paul W. Eloe (0000-0002-6590-9931), and Bo Zhang

Submissions from 1999

Comparison of eigenvalues for discrete Lidstone boundary value problems, John M. Davis, Paul W. Eloe, and Johnny Henderson

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Triple positive solutions and dependence on higher order derivatives, John M. Davis, Paul W. Eloe, and Johnny Henderson

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Triple positive solutions for multipoint conjugate boundary value problems, John M. Davis, Paul W. Eloe, and Johnny Henderson

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Inequalities for solutions of multipoint boundary value problems, Paul W. Eloe and Johnny Henderson

Twin solutions for nonlinear multipoint conjugate boundary value problems, Paul W. Eloe and Johnny Henderson

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On The Decomposition of Order-separable Posets of Countable Width into Chains, Gary Gruenhage and Joe Mashburn

Submissions from 1998

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Refracting System for Annular Gaussian-to-Bessel Beam Transformation, Muhammad Arif, Meer M. Hossain, Abdul Ahad S. Awwal, and Muhammad Islam

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Two-Element Refracting System for Annular Gaussian-to-Bessel Beam Transformation, Muhammad Arif, Meer M. Hossain, Abdul Ahad S. Awwal, and Muhammad Islam

Monotone and quadratic convergence of approximate solutions of ordinary differential equations with impulse, Vidya Doddaballapur and Paul W. Eloe

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Quadratic convergence of approximate solutions of two-point boundary value problems with impulse, Vidya Doddaballapur, Paul W. Eloe, and Yongzhi Zhang

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A generalization of concavity for finite differences, Paul W. Eloe

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Positive solutions of boundary-value problems for disfocal ordinary differential equations, Paul W. Eloe

Positive solutions and nonlinear (k,n-k) conjugate eigenvalue problems, Paul W. Eloe and Johnny Henderson

Positive solutions of boundary value problems for ordinary differential equations with impulse, Paul W. Eloe and Johnny Henderson

Singular nonlinear multipoint conjugate boundary value problems, Paul W. Eloe and Johnny Henderson

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Multiple positive solutions for difference equations, Paul W. Eloe, Johnny Henderson, and Eric R. Kaufmann

Positive solutions and conjugate points for a boundary value problem with impulse, Paul W. Eloe and Michael Sokol

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A quadratic monotone iteration scheme for two-point boundary value problems for ordinary differential equations, Paul W. Eloe and Yongzhi Zhang

Submissions from 1997

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A boundary value problem for a system of ordinary differential equations with impulse effects, Paul W. Eloe and Johnny Henderson

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Inequalities based on a generalization of concavity, Paul W. Eloe and Johnny Henderson

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Positive solutions and nonlinear multipoint conjugate eigenvalue problems, Paul W. Eloe and Johnny Henderson

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Positive solutions for (n-1,1) conjugate boundary value problems, Paul W. Eloe and Johnny Henderson

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Singular nonlinear (k,n-k) conjugate boundary value problems, Paul W. Eloe and Johnny Henderson

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Singular nonlinear (n-1,1) conjugate boundary value problems, Paul W. Eloe and Johnny Henderson

Positive solutions of three point boundary value problems, Paul W. Eloe and Janet McKelvey

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Almost Periodic Solutions of Nonlinear Integral Equations, Muhammad Islam

Submissions from 1996

Right focal boundary value problems with impulse effects, Paul W. Eloe, Johnny Henderson, and Tarique Khan

Positive solutions for two-point boundary value problems, Paul W. Eloe, Johnny Henderson, and Patricia J. Y. Wong

A singular boundary value problem for a right disfocal linear differential operator, Paul W. Eloe and Eric R. Kaufmann

Sign properties of Green's functions for difference equations, Paul W. Eloe and Timothy Peil

Submissions from 1995

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Bifurcation from infinity and higher order ordinary differential equations, Joe Coyle, Paul W. Eloe, and Johnny Henderson

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Positive solutions for higher order ordinary differential equations, Paul W. Eloe and Johnny Henderson

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Singular boundary value problems for quasi-differential equations, Paul W. Eloe and Johnny Henderson

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Multipoint boundary value problems for functional differential equations, Paul W. Eloe (0000-0002-6590-9931), Johnny Henderson, and Denise Taunton

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Stability Properties and Integrability of the Resolvent of Linear Volterra Equations, Muhammad Islam and Paul W. Eloe (0000-0002-6590-9931)

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A Note on Reordering Ordered Topological Spaces and the Existence of Continuous, Strictly Increasing Functions, Joe Mashburn

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The convergence of iterative solutions to the electric field integral equation, Daniel D. Reuster, Gary A. Thiele, and Paul W. Eloe

Submissions from 1994

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Focal point characterizations and comparisons for right focal differential operators, Paul W. Eloe and Johnny Henderson

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Multipoint boundary value problems for ordinary differential systems, Paul W. Eloe and Johnny Henderson

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A unique limiting Green's function for a class of singular boundary value problems, Paul W. Eloe and Eric R. Kaufmann

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Sign properties of Green's functions for a family of two-point boundary value problems, Paul W. Eloe and Jerry Ridenhour

Submissions from 1993

Differentiability with respect to boundary conditions and deviating argument for functional-differential systems, Jeffrey Ehme, Paul W. Eloe, and Johnny Henderson

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Existence of solutions for some singular higher order boundary value problems, Paul W. Eloe and Johnny Henderson

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Focal points and comparison theorems for a class of two-point boundary value problems, Paul W. Eloe and Johnny Henderson

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On Infinite Delay Integral Equations Having Nonlinear Perturbations, Muhammad Islam

Submissions from 1992

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Positive solutions and conjugate points for multipoint boundary value problems, Paul W. Eloe, Darrel Hankerson, and Johnny Henderson

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Positive solutions and J-focal points for two-point boundary value problems, Paul W. Eloe, Darrel Hankerson, and Johnny Henderson

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Modified Signed-Digit Trinary Arithmetic Using Optical Symbolic Substitution, Muhammad Islam, A. A. S. Awwal, and Mohammad A. Karim

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Nonlinear Integrodifferential Equations and A Priori Bounds on Periodic Solutions, Muhammad Islam, T. A. Burton, and Paul W. Eloe (0000-0002-6590-9931)

Submissions from 1991

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Singular nonlinear boundary value problems for higher order ordinary differential equations, Paul W. Eloe and Johnny Henderson

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Bounded Solutions and Periodic Solutions of Volterra Equations With Infinite Delay, Muhammad Islam

Submissions from 1990

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Periodic Solutions of Linear Integrodifferential Equations, Muhammad Islam, T. A. Burton, and Paul W. Eloe (0000-0002-6590-9931)