• 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
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
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
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
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
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
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
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
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
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
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
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
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
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