• 5061 Citations
  • 37 h-Index
1976 …2020
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Research Output 1976 2019

  • 5061 Citations
  • 37 h-Index
  • 132 Article
  • 3 Conference contribution
  • 1 Chapter
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Article
1976
2 Citations (Scopus)

Bounded oscillation in a class of functional differential equations

Smith, H., 1976, In : Journal of Mathematical Analysis and Applications. 56, 1, p. 223-232 10 p.

Research output: Contribution to journalArticle

Functional Differential Equations
Differential equations
Oscillation
Class
1977
32 Citations (Scopus)

Fixed point techniques in a cone with applications

Gatica, J. A. & Smith, H., Nov 1 1977, In : Journal of Mathematical Analysis and Applications. 61, 1, p. 58-71 14 p.

Research output: Contribution to journalArticle

Banach spaces
Ordinary differential equations
Boundary value problems
Integral equations
Mathematical operators
35 Citations (Scopus)

On periodic solutions of a delay integral equation modelling epidemics

Smith, H., Mar 1977, In : Journal of Mathematical Biology. 4, 1, p. 69-80 12 p.

Research output: Contribution to journalArticle

Delay Equations
Integral equations
Periodic Solution
Integral Equations
Qualitative Behavior
1978
4 Citations (Scopus)

Periodic solutions for a class of epidemic equations

Smith, H., Jun 15 1978, In : Journal of Mathematical Analysis and Applications. 64, 2, p. 467-479 13 p.

Research output: Contribution to journalArticle

Global Bifurcation
Delay Equations
Integral equations
Periodic Solution
Integral Equations
30 Citations (Scopus)

Positive solutions and conjugate points for systems of differential equations

Schmitt, K. & Smith, H., 1978, In : Nonlinear Analysis. 2, 1, p. 93-105 13 p.

Research output: Contribution to journalArticle

Disconjugacy
Conjugate points
Second-order Systems
Positive Operator
System of Differential Equations
1979
33 Citations (Scopus)

On eigenvalue problems for nondifferentiable mappings

Schmitt, K. & Smith, H., 1979, In : Journal of Differential Equations. 33, 3, p. 294-319 26 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Periodic solutions of an epidemic model with a threshold

Smith, H., Dec 1979, In : Rocky Mountain Journal of Mathematics. 9, 1, p. 131-142 12 p.

Research output: Contribution to journalArticle

Epidemic Model
Periodic Solution
1980
6 Citations (Scopus)

A note on disconjugacy for second order systems

Smith, H., 1980, In : Pacific Journal of Mathematics. 89, 2, p. 447-452 6 p.

Research output: Contribution to journalArticle

Disconjugacy
Second-order Systems
Non-negative
Valid
Sufficient
9 Citations (Scopus)

A uniqueness theorem for flxedp oints

Smith, H. & Stuart, C. A., 1980, In : Proceedings of the American Mathematical Society. 79, 2, p. 237-240 4 p.

Research output: Contribution to journalArticle

Banach spaces
Uniqueness Theorem
Fixed point
Completely Continuous
Eigenvalue
14 Citations (Scopus)

Periodic solutions of some nonlinear delay-differential equations

Martelli, M., Schmitt, K. & Smith, H., 1980, In : Journal of Mathematical Analysis and Applications. 74, 2, p. 494-503 10 p.

Research output: Contribution to journalArticle

Delay Differential Equations
Nonlinear Differential Equations
Periodic Solution
Differential equations
1981
3 Citations (Scopus)

Nonresonant periodic perturbation of the hopf bifurcation

Smith, H., Jan 1 1981, In : Applicable Analysis. 12, 3, p. 173-195 23 p.

Research output: Contribution to journalArticle

Hopf bifurcation
Autonomous Systems
Hopf Bifurcation
Periodic Solution
Perturbation
1982
3 Citations (Scopus)

Fredholm alternatives for nonlinear differential equations

Schmitt, K. & Smith, H., Sep 1982, In : Rocky Mountain Journal of Mathematics. 12, 4, p. 817-841 25 p.

Research output: Contribution to journalArticle

Fredholm Alternative
Nonlinear Differential Equations
5 Citations (Scopus)

On the basin of attraction of a perturbed attractor

Smith, H., 1982, In : Nonlinear Analysis. 6, 9, p. 911-917 7 p.

Research output: Contribution to journalArticle

Basin of Attraction
Domain of Attraction
Attractor
1983
150 Citations (Scopus)

Infinite subharmonic bifurcation in an SEIR epidemic model

Schwartz, I. B. & Smith, H., Dec 1983, In : Journal of Mathematical Biology. 18, 3, p. 233-253 21 p.

Research output: Contribution to journalArticle

Subharmonic Solutions
Subharmonics
Domain of Attraction
Epidemic Model
Immunity
44 Citations (Scopus)

Multiple stable subharmonics for a periodic epidemic model

Smith, H., Jun 1983, In : Journal of Mathematical Biology. 17, 2, p. 179-190 12 p.

Research output: Contribution to journalArticle

Subharmonic Solutions
Si
Subharmonics
Epidemic Model
Annual
55 Citations (Scopus)

Subharmonic bifurcation in an S-I-R epidemic model

Smith, H., Jun 1983, In : Journal of Mathematical Biology. 17, 2, p. 163-177 15 p.

Research output: Contribution to journalArticle

Si
Subharmonics
Epidemic Model
oscillation
Bifurcation
1986
149 Citations (Scopus)

Cooperative systems of differential equations with concave nonlinearities

Smith, H., 1986, In : Nonlinear Analysis. 10, 10, p. 1037-1052 16 p.

Research output: Contribution to journalArticle

Cooperative Systems
System of Differential Equations
Differential equations
Nonlinearity
9 Citations (Scopus)

Normal forms for periodic systems

Smith, H., Feb 1 1986, In : Journal of Mathematical Analysis and Applications. 113, 2, p. 578-600 23 p.

Research output: Contribution to journalArticle

Time varying systems
Periodic Systems
Normal Form
61 Citations (Scopus)

ON THE ASYMPTOTIC BEHAVIOR OF A CLASS OF DETERMINISTIC MODELS OF COOPERATING SPECIES.

Smith, H., Jun 1986, In : SIAM Journal on Applied Mathematics. 46, 3, p. 368-375 8 p.

Research output: Contribution to journalArticle

Deterministic Model
Ordinary differential equations
Nonlinear systems
Asymptotic Behavior
Perron-Frobenius Theory
78 Citations (Scopus)

Periodic competitive differential equations and the discrete dynamics of competitive maps

Smith, H., Sep 15 1986, In : Journal of Differential Equations. 64, 2, p. 165-194 30 p.

Research output: Contribution to journalArticle

Differential equations
48 Citations (Scopus)

Periodic orbits of competitive and cooperative systems

Smith, H., 1986, In : Journal of Differential Equations. 65, 3, p. 361-373 13 p.

Research output: Contribution to journalArticle

Competitive System
Cooperative Systems
Periodic Orbits
Orbits
Three-dimensional
1987
13 Citations (Scopus)

A classification theorem for three dimensional competitive systems

Smith, H. & Waltman, P., 1987, In : Journal of Differential Equations. 70, 3, p. 325-332 8 p.

Research output: Contribution to journalArticle

Competitive System
Three-dimensional
Theorem
153 Citations (Scopus)

Monotone semiflows generated by functional differential equations

Smith, H., Mar 15 1987, In : Journal of Differential Equations. 66, 3, p. 420-442 23 p.

Research output: Contribution to journalArticle

Semiflow
Functional Differential Equations
Monotone
70 Citations (Scopus)

Oscillations and multiple steady states in a cyclic gene model with repression

Smith, H., Jun 1987, In : Journal of Mathematical Biology. 25, 2, p. 169-190 22 p.

Research output: Contribution to journalArticle

oscillation
Physiological Feedback
Genes
Oscillation
Gene
1988
172 Citations (Scopus)

Systems of ordinary differential equations which generate an order preserving flow. A survey of results

Smith, H., Mar 1988, In : SIAM Review. 30, 1, p. 87-113 27 p.

Research output: Contribution to journalArticle

System of Ordinary Differential Equations
Ordinary differential equations
Partial ordering
Feedback
Negative Feedback
1989
1 Citation (Scopus)

Competing subcommunities of mutualists

Smith, H., 1989, In : Computers and Mathematics with Applications. 18, 10-11, p. 949-957 9 p.

Research output: Contribution to journalArticle

Convergence to Equilibrium
Ecosystem
Persistence
Ecosystems
Time Delay
17 Citations (Scopus)

Competition in the gradostat: the role of the communication rate

Smith, H. & Tang, B., Apr 1989, In : Journal of Mathematical Biology. 27, 2, p. 139-165 27 p.

Research output: Contribution to journalArticle

Microorganisms
Nutrients
Vessel
Chemostats
microorganisms
1990
351 Citations (Scopus)

Abstract functional differential equations and reaction-diffusion systems

Martin, R. H. & Smith, H., 1990, In : Transactions of the American Mathematical Society. 321, 1, p. 1-44 44 p.

Research output: Contribution to journalArticle

Abstract Differential Equations
Banach spaces
Lyapunov functions
Functional Differential Equations
Linear equations
3 Citations (Scopus)

A discrete Lyapunov function for a class of linear differential equations

Smith, H., 1990, In : Pacific Journal of Mathematics. 144, 2, p. 345-360 16 p.

Research output: Contribution to journalArticle

System of Ordinary Differential Equations
Linear differential equation
Lyapunov Function
Linear Systems
Trajectory
7 Citations (Scopus)

Microbial growth in periodic gradostats

Smith, H., Sep 1990, In : Rocky Mountain Journal of Mathematics. 20, 4, p. 1173-1194 22 p.

Research output: Contribution to journalArticle

46 Citations (Scopus)
Semiflow
Functional Differential Equations
Ordinary differential equations
Monotone
Differential equations
165 Citations (Scopus)

The Poincare-Bendixson theorem for monotone cyclic feedback systems

Mallet-Paret, J. & Smith, H., Oct 1990, In : Journal of Dynamics and Differential Equations. 2, 4, p. 367-421 55 p.

Research output: Contribution to journalArticle

Poincaré-Bendixson Theorem
Feedback Systems
Biological Systems
Monotone
Model
1991
22 Citations (Scopus)

Competition in an n-vessel gradostat

Smith, H., Tang, B. & Waltman, P., Oct 1991, In : SIAM Journal on Applied Mathematics. 51, 5, p. 1451-1471 21 p.

Research output: Contribution to journalArticle

Bifurcation (mathematics)
Coexistence
Vessel
Dynamical systems
Monotone Dynamical System
12 Citations (Scopus)
Chemical activation
Neural networks
2 Citations (Scopus)
Equilibrium Distribution
Singular Perturbation
Vessel
mathematical models
biogeography
17 Citations (Scopus)
Infinite Delay
Lotka-Volterra System
Global Stability
Patch
Unbounded Delay
37 Citations (Scopus)

Global stability in diffusive delay Lotka-Volterra systems

Kuangt, Y., Smith, H. & Schmitt, K., 1991, In : Differential and Integral Equations. 4, 1, p. 117-128 12 p.

Research output: Contribution to journalArticle

Lotka-Volterra System
Delay Systems
Global Asymptotic Stability
Asymptotic stability
Global Stability
112 Citations (Scopus)

Reaction-diffusion systems with time delays: Monotonicity, invariance, comparison and convergence

Martin, R. H. & Smith, H., 1991, In : Journal fur die Reine und Angewandte Mathematik. 1991, 413, p. 1-35 35 p.

Research output: Contribution to journalArticle

Invariance
Reaction-diffusion System
Monotonicity
Time Delay
Time delay
30 Citations (Scopus)

Stable periodic solutions for the hypercycle system

Hofbauer, J., Mallet-Paret, J. & Smith, H., Jul 1991, In : Journal of Dynamics and Differential Equations. 3, 3, p. 423-436 14 p.

Research output: Contribution to journalArticle

Periodic Orbits
Periodic Solution
Omega Limit Set
Reactor
Orbit
98 Citations (Scopus)

Strongly order preserving semiflows generated by functional differential equations

Smith, H. & Thieme, H., 1991, In : Journal of Differential Equations. 93, 2, p. 332-363 32 p.

Research output: Contribution to journalArticle

Differential equations
19 Citations (Scopus)

The gradostat: A model of competition along a nutrient gradient

Smith, H. & Waltman, P., Dec 1991, In : Microbial Ecology. 22, 1, p. 207-226 20 p.

Research output: Contribution to journalArticle

vessel
mathematical theory
Food
nutrient
nutrients
1992
60 Citations (Scopus)

Slowly oscillating periodic solutions of autonomous state-dependent delay equations

Kuang, Y. & Smith, H., 1992, In : Nonlinear Analysis. 19, 9, p. 855-872 18 p.

Research output: Contribution to journalArticle

State-dependent Delay
Delay Equations
Periodic Solution
Oscillation
1993
10 Citations (Scopus)
Lotka-Volterra
Delay Systems
Type Systems
Instantaneous
Negative Feedback
15 Citations (Scopus)
Global Solution
Existence and Uniqueness
Model
122 Citations (Scopus)

Global Stability for Infinite Delay Lotka-Volterra Type Systems

Kuang, Y. & Smith, H., Jun 1993, In : Journal of Differential Equations. 103, 2, p. 221-246 26 p.

Research output: Contribution to journalArticle

Infinite Delay
Lotka-Volterra System
Global Stability
Type Systems
Sufficient Conditions
53 Citations (Scopus)
Structured Populations
Delay Equations
Population Model
Functional Differential Equations
Differential equations
1994
24 Citations (Scopus)
Uniform Persistence
Structured Populations
Global Attractor
Population Model
Functional Differential Equations
49 Citations (Scopus)

Competition for a single limiting resource in continuous culture: The variable-yield model

Smith, H. & Waltman, P., Aug 1994, In : SIAM Journal on Applied Mathematics. 54, 4, p. 1113-1131 19 p.

Research output: Contribution to journalArticle

Nutrients
Limiting
Resources
Competitive Exclusion
Asymptotic Behavior of Solutions
50 Citations (Scopus)

Stable Periodic Orbits for a Class of Three Dimensional Competitive Systems

Zhu, H. R. & Smith, H., May 1994, In : Journal of Differential Equations. 110, 1, p. 143-156 14 p.

Research output: Contribution to journalArticle

Competitive System
Equilibrium Point
Periodic Orbits
Orbits
Three-dimensional
1995
152 Citations (Scopus)

Asymptotically autonomous semiflows: Chain recurrence and lyapunov functions

Mischaikow, K., Smith, H. & Thieme, H., 1995, In : Transactions of the American Mathematical Society. 347, 5, p. 1669-1685 17 p.

Research output: Contribution to journalArticle

Chain Recurrence
Semiflow
Lyapunov functions
Lyapunov Function
Omega Limit Set