Theodore Burton

Department of Mathematics
Southern Illinois University

Reprints and Preprints of Professional Papers

The following papers are available as.pdf files.

  1. Integral Equations, Implicit Functions, and Fixed Points
      Proceedings of the A.M.S., 124 (1996), 2383-2390
      Download the file BU-IEIF.pdf

  2. Almost Periodic Solutions of Volterra Equations and Attractivity, with T. Furumochi
      Journal of Math. Analysis and Applications, 198 (1996), 581-599
      Download the file BU-APSVE.pdf

  3. Asymptotic stability of second order ordinary, functional, and partial differential equations,with L. Hatvani
      J. Math. Anal. Appl., , 176(1993), 261-281
      Download the file BU-ASSO.pdf

  4. Examples of Lyapunov functionals for non-differentiated equations
      Proceedings of the First World Congress of Nonlinear Analysts, ed. V. Lakshmikantham, (1996), 1203-1214
      Download the file LFNE.pdf

  5. A stability theory for integral equations, with T. Furumochi
      J. Integral Equations and Applications, 6 (1994), 445-477
      Download the file BU-STIE.pdf

  6. Averaged Neural Networks
      Neural Networks, 6 (1993), 677-680
      Download the file AVGNNT.pdf

  7. Boundedness of solutions of integrodifferential equations
      Annals of Differential Equations, 9 (1993), 395-408
      Download the file BU-BSIE.pdf

  8. On the existence of periodic solutions of some nonlinear functional differential equations with unbounded delay, with L. Hatvani
      J. Nonlinear Analysis, 16 (1991), 389-398
      Download the file EXISTPRS.pdf

  9. Periodic solutions of abstract differential equations with infinite delay, with Bo Zhang
      J. Differential Equations, 90 (1991), 357-396
      Download the file BUPSWID1.pdf

  10. Asymptotic stability for functional differential equations, with G. Makay
      Acta Math. Hungar.,65 (1994), 243-251
      Download the file BMSAVE.pdf

  11. The search for periodic solutions in neural networks
      World Scientific Pub. Co WSSIAA, 4 (1995), 117-126
      Download the file BU-SPS.pdf

  12. Periodic solutions of a Volterra equation and robustness, with T. Furumochi
      Nonlinear Analysis, 25 (1995), 1199-1219
      Download the file BU-PSVE.pdf

  13. Periodic solutions of Volterra equations and attractivity, with T. Furumochi
      Dynamic Systems and Applications, 3 (1994), 583-598
      Download the file BU-PSVEA.pdf

  14. Stability in several measures and a differential inequality for a partial integral equation, with T. Furumochi and Q. Huang
      Nonlinear Analysis 25 (1995), 885-898
      Download the file BU-SSM.pdf

  15. An extension of Krasovskii's stability theory
      Engineering Cybernetics, 1 (1993), 44-51
      Download the file BU-KRSV1.pdf

  16. Boundedness and periodicity in integral and integro-differential equations
      Differential Equations and Dynamical Systems, 1 (1993), 161-172
      Download the file BU-BPIIE.pdf

  17. Liapunov functionals and periodicity in integral equations
      Tohoku Math. J., 46 (1994), 207-220
      Download the file BU-LFPIE.pdf

  18. Liapunov theory for functional differential equations, with R. Hering
      Rocky Mountain J. Math., 24 (1994), 3-17
      Download the file BU-LTFDE.pdf

  19. Admissible controls in a PDE of Lurie type
      PDE's with Wiener and Hale, eds, Pittman Research Notes , (1992), 16-28
      Download the file BU-ACPDE.pdf

  20. Differential inequalities and existence theory for differential, integral, and delay equations
      in Comparison Methods and Stqability Theory, Dekker, ed by Xinzhi Liu and David Siegel, (1994), 35-56
      Download the file BU-ETDI.pdf

  21. Integral equations with a delay
      Acta. Math. Hungarica, (1996), 233-242
      Download the file BU-IED.pdf

  22. A wave equation viewed as an ordinary differential equation
      Contemporary Mathematics (Graef and Hale eds) 129 (1992), 23--41
      Download the file WEVODE.pdf

  23. A general stability result of Marachkov type
      Ann. Diff. Eqs., 8 (1992), 148-157
      Download the file BU-GSRMT.pdf

  24. Functional Differential equations and Jensen's inequality, with L Becker and S Zhang
      J. Math. Anal. Appl., 138 (1989), 137-156
      Download the file bufdeji.pdf

  25. Upper and lower bounds for Liapunov functionals, with A Casal and A Somolinos
      Funkcialaj Ekvacioj, 32 (1989), 23-55
      Download the file bcs.pdf

  26. Stability theorems for nonautonomous functional differential equations by Liapunov functionals, with L. Hatvani
      Tohoku Math. J. 41 (1989), 65-104
      Download the file bu-stnf.pdf

  27. The nonlinear wave equation as a Lienard equation
      Funkcialaj Ekvacioj, 34 (1991), 529-545
      Download the file Bu-nwe.pdf

  28. Periodic and asymptotically periodic solutions of Volterra integral equations, with T. Furumochi
      Funkcialaj Ekvacioj, 39 (1996), 87-107
      Download the file BU-PAPS.pdf

  29. An integral equation of advanced and retarded type,
      Dynamic Systems and Applications, 5(1996), 183-188.
      Download the file bu-ieart.pdf

  30. A fixed point theorem of Krasnosel'skii-Schaefer type with Colleen Kirk,
      Mathematische Nachrichten, 189(1998), 23-31.
      Download the file bk-afpt.pdf

  31. Basic neutral integral equations of advanced type,
      Nonlinear Analysis, 31(1998), 295-310.
      Download the file bu-bnie.pdf

  32. Krasnoselskii's inversion principle and fixed points,
      Nonlinear Analysis, 30(1997), 3975-3986.
      Download the file bu-rev.pdf

  33. Linear integral equations and periodicity,
      Ann. Differential Equations 13(1997), 313-326.
      Download the file bu-liep.pdf

  34. A fixed-point theorem of Krasnoselskii,
      Appl. Math. Lett. 11(1998), 85-88.
      Download the file bu-fptk.pdf

  35. An existence theorem for a neutral equation,
      Nonlinear Studies 5(1998), 1-6.
      Download the file BU-SSM.pdf

  36. Marachkov type stability results for functional differential equations, with G. Makay,
      E. J. Qualitative Theory of Diff. Eq. 1(1998), 1-17.
      Download the file bmlast.pdf

  37. Periodicity in delay equations by direct fixed point mappings, with Bo Zhang,
      Differential Equations and Dynamical Systems, 6(1998), 413-424.
      Download the file pdedfpm.pdf

  38. Periodic solutions of a neutral integro-differential equation, with Tetsuo Furumochi,
      Funkcialaj Ekvacioj, 41(1998), 327-336.
      Download the file bu-psnie.pdf

  39. Periodicity by a priori bounds and existence,
      Dynamics of Continuous, Discrete and Impulsive Systems, 5(1999) 381-394.
      Download the file BU-PPBE.pdf

  40. Neutral integral equations of retarded type, with R. Hering,
      Nonlinear Analysis 41(2000), 545-572.
      Download the file Hering3.pdf

  41. Existence theorems and periodic solutions of neutral integral equations, with Tetsuo Furumochi,
      Nolinear Analysis 43(2001)527-546.
      Download the file ETPSNE.pdf

  42. Uniform boundedness by averaging, with Bo Zhang,
      Acta Math. Hungarica 92(4) (2001),263-283.
      Download the file bobu-uba.pdf

  43. A note on stability by Schauder's theorem, with Tetsuo Furumochi,
      Funkcialaj Ekvacioj 44(2001), 73-82.
      Download the file bf-nsst.pdf

  44. Fixed points and problems in stability theory, with Tetsuo Furumochi,
      Dynamical Systems and Appl. 10(2001), 89-116.
      Download the file fpapist2.pdf

  45. Krasnoselskii's fixed point theorem and stability, with Tetsuo Furumochi,
      Nonlinear Analysis 49(2002), 445-454.
      Download the file krastab.pdf

  46. Asymptotic stability and boundedness for functional differential equations, with Qichang Huang,
      Acta Math. Sinica, 13(1997), 363-372.
      Download the file bu-asbfd.pdf

  47. Liapunov functionals, fixed points, and stability by Krasnoselskii's theorem,
      Nonlinear Studies 9(2001), 181-190.
      Download the file Lffpskt1.pdf

  48. Stability by fixed point theory or Liapunov theory: A comparison,
      Fixed Point Theory 4(2003), 15-32.
      Download the file sfptltac.pdf

  49. Asymptotic behavior of solutions of functional differential equations by fixed point theorems, with Tetsuo Furumochi,
      Dynamic Systems Appl. 11(2002), 499-521.
      Download the file absfdef2.pdf

  50. Perron-type stability theorems for neutral equations,
      Nonlinear Analysis 55(2003), 285-297.
      Download the file Ptstne1.pdf

  51. Fixed points and stability of an integral equation: nonuniqueness, with Bo Zhang,
      Appl. Math. Letters 17(2004), 839-846.
      Download the file fpsiebo6.pdf

  52. Stability by fixed point methods for highly nonlinear delay equations,
      Fixed Point Theory 5(2004), 3-20.
      Download the file sfpmhnde.pdf

  53. Fixed points and stability of a nonconvolution equation,
      Proc. Amer. Math. Soc. 132(2004), 3679-3687.
      Download the file fpsnce1.pdf

  54. Jensen's Inequality and Liapunov's Direct Method, with Leigh Becker,
      Cubo A Mathematical Journal 6, 3(2004), pp. 65-87.
      Download the file Jensen.pdf

  55. Asymptotic behavior of nonlinear functional differential equations by Schauder's theorem with Tetsuo Furumochi,
      Nonlinear Studies 12(2005), 73-84.
      Download the file abnfd32.pdf

  56. Stability and fixed points: Addition of terms,
      Dynamic Systems and Applications 13(2004), 459-478.
      Download the file sfpat1.pdf

  57. Stability and Periodic Solutions of Ordinary and Functional Differential Equations,
      Dover, New York, 2005.   (This is a corrected reprinting of the 1985 edition by Academic Press.)
      To order, go to

  58. Volterra Integral and Differential Equations,
      Second Edition, Elsevier, Amsterdam, 2005. (This is the second edition of the 1985 edition by Academic Press.)
      To order, go to

  59. Fixed Points, Stability, and Exact Linearization,
      Nonlinear Analysis 61(2005), 857-870.
      Download the file fpsael.pdf.

  60. Fixed Points, Stability, and Harmless Perturbations,
      Fixed Point Theory and Applications 1(2005), 35-46.
      Download the file fpshp1.pdf.

  61. Fixed Points, Volterra Equations, and Becker's Resolvent,
      Acta. Math. Hungar. 108(2005), 261-281.
      Download the file fpvebr.pdf.

  62. Lienard Equations, Delays, and Harmless Perturbations,
      Fixed Point Theory 5(204), 209-223.
      Download the file ledahp.pdf.

  63. Stability, fixed points and inverses of delays, with Leigh C. Becker,
      Proc. Roy. Soc. Edinburgh Sect. A 136(2006), 245-275.
      Download sfpidrev1.pdf

  64. Integral equations, Volterra equations, and the remarkable resolvent: contractions,
      Electron. J. Qual. Theory Differ. Equ. 2006, No. 2, 17pp., (electronic)
      Download ieveatrr1.pdf

  65. Stability by Fixed Point Theory for Functional Differential Equations,
      Dover Publications, New York, Oct. 2006.
      To order, go to or

  66. The Case for Stability by Fixed Point Theory,
      Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 13B (2006), suppl., 253-263.
      Download Tcfsbfpt.pdf

  67. The Lurie control satisfies a Lienard equation, with Alfredo Somolinos.
     Dyn. Contin. Discrete Impuls. Syst. Ser. B. Appl. Algorithms. 14(2007), 625-640.
      Download burSom.pdf

  68. Integral equations, large forcing, strong resolvents.
     Carpathian J. Math. 23(2007), 1-10.
     Download ielfsr.pdf

  69. Integral equations, large and small forcing functions: periodicity.
     Math. Comput. Modelling 45(2007), 1363-1375.
     Download L-ielasffp.pdf

  70. Integral equations with contrasting kernels.
     E. J. Qual. Theory Diff. Equ. 2(2008), 1-22.
     Download iewck.pdf

  71. Integral equations, L^p-forcing, remarkable resolvent: Liapunov functionals.
     Nonlinear Anal. 68(2007), 35-46.
     Download LA-ielfrr.pdf

  72. Scalar nonlinear integral equations.
    Tatra Mountains Math. Publications 38(2007), 41-56.
    Download snie.pdf

  73. Integral equations, periodicity, and fixed points.
    Fixed Point Theory 9(2008), 47-65
    Download July07.pdf

  74. Liapunov Functionals for Integral Equations.
    Trafford, Victoria, British Columbia, Canada, 2008.
    Order online at

  75. Qualitative Properties of Solutions of Integral Equations, with J. R. Haddock.
    Nonlinear Analysis 71(2009), 5712-5723.
    Download iebh4-16-9.pdf

  76. A Liapunov Functional for a Linear Integral Equation.
    Elect. J. Qual. Theory Diff. Equations 10(2010), 1-10.
    Download alffalien.pdf

  77. A Liapunov Functional for a Singular Integral Equation .
    Nonlinear Analysis 73(2010), 3873-3882.
    Download alffasie-3.pdf

  78. Six integral equations and a flexible Liapunov functional.
    Trudy Instituta Matematiki i Mekhaniki Ur0 RAN, 16(2010), No. 5, 241-252.
    Download Burton2.pdf.

  79. Resolvents, integral equations, limit sets, with D.P. Dwiggins.
    Mathematica Bohemica, 135(2010), No. 4, pp. 337-354.
    Download Riels-15.pdf.

  80. Liapunov Functionals, Convex Kernels, and Strategy.
    Nonlinear Dynamics and Systems Theory 10(2010), 325-337.
    Download Lfcks-1.pdf

  81. Parallel Theories of Integral Equations, with J. R. Haddock,
    Nonlinear Studies 17 (2010), 177-197.
    Download Ptoie-2.pdf

  82. Periodic Solutions of Singular Integral Equations, with Bo Zhang.
    Nonlinear Dynamics and Systems Theory 11 (2011), 113-123.
    Download Psosie-L.pdf
  83. Smoothed Integral Equations, Burton, T. A. and Dwiggins, D. P.,
    J. Math. Anal Appl. 377 (2010), 319-335. 
    Download SIE-final.pdf

  84. Kernel-Resolvent Relations for an Integral Equation, Burton, T. A., Tatra
    Mt. Math. Publ. 48 (2011), 25-40. 
    Download KrrfaieS2.pdf

  85. Fractional Differential Equations and Lyapunov Functionals, Burton, T. A.,
    Nonlinear Analysis 74 (2011), 5648-5662. 
    Download Fdealf-11.pdf

  86. L^p-solutions of singular integrodifferential equations, with Ioannis K. Purnaras,
    J. Math. Anal. Appl. 386 (2012), 830-841
    Download the file LpsosieV4b.pdf

  87. Singular integral equations, Liapunov functionals, and resolvents, with L. C. Becker and  I. K. Purnaras,
    Nonlinear Analysis 75 (2012), 3277-3291  
    Download the file Sielfar-R2.pdf

  88. Bounded and periodic solutions of integral equations, with Bo Zhang,
    CUBO A Mathematical Journal 14 (No. 01), 55-79.
    Download the file Bapsoie.pdf.
  89. L^p Solutions of Fractional Differential Equations, with Bo Zhang,
    Nonlinear Studies 19 (2012), pp. 161-177
    Download the file Lpsofde-6d.pdf.

  90. Fractional Equations and Generalizations of Schaefer's and Krasnoselskii's Fixed Point Theorems, with Bo Zhang,
    Nonlinear Analysis 75 (2012), 6485-6495.
    Download the file Fefpac-7.pdf.

  91. Liapunov Functionals for Integral Equations, Trafford, Victoria, B.C., Canada, 2008.
    Download Viburt.pdf

  92. Asymptotically Periodic Solutions of Fractional Differential Equations, with Bo Zhang,
    Dynamics of Continuous, Discrete, and Impulsive Systems, Series A: Mathematical Analysis 20 (2013), 1-21.
    Download the file Apsofde-5.pdf.

  93. Singular Integro-differential Equations with Small Kernels, T. A. Burton and I. K. Purnaras,
    J. Integral Equations and Applications 25(2013), 1-20
    Download the file Sidewsk_7AB.pdf

  94. A Unification Theory of Krasnoselskii for Differential Equations, with I. K. Purnaras,
    Nonlinear Analysis \textbf{89} (2013) 121-133.
    Download the file Autok-14.pdf

  95. Volterra's Linear Equation and Krasnoselskii's Hypothesis, with I. K. Purnaras,
    Communications in Applied Analysis \textbf{17} no. 3 and 4, (2013) 529-554.
    Download the file Laks.pdf

  96. Fractional Equations and a Theorem of Brouwer-Schauder Type,
    Fixed Point Theory \textbf{14} no. 1 (2013) 91-96
    Download the file Brouwer-Schauder-1.pdf

  97. Fixed Points and Fractional  Differential Equations: Examples, with Bo Zhang,
    Fixed Point Theory \textbf{14} no. 2 (2013) 313 -326.
    Download the file Fpafde-8.pdf

  98. A Schauder-type fixed point theorem, with Bo Zhang
    J. Math. Anal. Appl. 417(2014), no. 2, 552-558.
    Download the file Astfpt-12.pdf

  99. Krasnoselskii's unification, Volterra's integrodifferential equation, and the method of Aizerman, with I. K. Purnaras
    Nonlinear. Stud. 21(2014), no. 1, 1-19
    Download the file Kuviatmoa-4B.pdf

  100. On the reduction of Krasnoselskii's theorem to Schauder's theorem, with Bo Zhang
    Appl. Math. Comput. 250(2015), 339-351
    Download the file Otrokttst-9.pdf

  101. Complementary equations: a fractional differential equation and a Volterra integral equation, with L. C. Becker and I. K. Purnaras
    Elect. J. Qual. Theory Diff. Eq. (2015), No. 12, 1-24
    Download the file lcBtaBikP1.pdf




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