
My research areas include dynamic equations and inequalities on time scales, differential equations, difference equations, qdifference equations, discrete dynamical systems, integral inequalities, asymptotic analysis, and boundary value problems. PDF versions of most of my papers are available below by clicking on the number of the paper. My coauthors and student coinquirers are listed in the lefthand column, with links to homepages (if available). According to MathSciNet (August 2013), these papers have been cited 681 times by 362 authors.
Journal publications and coauthored papers of Douglas R. Anderson

107. 
with Darin J. Ulness,
Properties of the Katugampola fractional derivative with potential application in quantum mechanics,
Journal of Mathematical Physics 56, 063502 (2015); doi: 10.1063/1.4922018.

106. 
with Richard I. Avery,
Existence of a solution to a conjugate boundary value problem applying a corollary of the omitted ray fixed point theorem,
Communications in Applied Analysis, 19 (2015), 403–412.

105. 
with Jenna Otto '16,
HyersUlam stability of linear differential equations with vanishing coefficients,
Communications in Applied Analysis, 19 (2015), 15–30.

104. 
with Richard I. Avery,
Fractionalorder boundary value problem with SturmLiouville boundary conditions,
Electronic Journal of Differential Equations, 2015 (2015), Number 29, 1–10.

103. 
with Richard I. Avery, Johnny Henderson, and Xueyan Liu,
Functional omitted ray fixed point theorem,
Journal of Fixed Point Theory, 2014 (2014), Article ID 7.

102. 
Hyers–Ulam stability of higherorder CauchyEuler dynamic equations on time scales,
Dynamic Systems & Applications, 23 (2014) 653–664.

101. 
with Richard I. Avery, Application of the omitted ray fixed point theorem,
Electronic Journal of Qualitative Theory of Differential Equations, 2014 (2014) No. 18, 1–9.

100. 
Existence of three solutions for a firstorder problem with nonlinear nonlocal boundary conditions,
Journal of Mathematical Analysis and Applications, 408 (2013) 318–323.

99. 
with Samir H. Saker, Interval oscillation criteria for forced EmdenFowler functional dynamic equations with oscillatory potential,
Science China Mathematics, 56:3 (2013) 561–576.

98. 
with Richard I. Avery, Johnny Henderson, and Xueyan Liu, Multiple fixed point theorems utilizing operators and functionals,
Communications in Applied Analysis, 16:3 (2012) 377–388.

97. 
with Ben Gates '13 and Dylan Heuer '13, HyersUlam stability of secondorder linear dynamic equations on time scales,
Communications in Applied Analysis, 16:3 (2012) 281–292.

96. 
with Richard I. Avery, Johnny Henderson, and Xueyan Liu, Fixed point theorem utilizing operators and functionals,
Electronic Journal of Qualitative Theory of Differential Equations, 2012, No. 12 (2012) 1–16.

95. 
with Richard I. Avery, Johnny Henderson, and Xueyan Liu, Existence of positive solutions of a second order right
focal boundary value problem,
Communications on Applied Nonlinear Analysis, 18:3 (2011) 41–51.

94. 
with Richard I. Avery, Johnny Henderson, and Xueyan Liu, Multiple fixed point theorems of operator type,
International Electronic Journal of Pure and Applied Mathematics, 3:2 (2011) 173–185.

93. 
with Steven Noren '11 and Brent Perreault '12, Young's integral inequality with upper and lower bounds,
Electronic Journal of Differential Equations, 2011 (2011), No. 74, 1–10.

92. 
with Richard I. Avery and Johnny Henderson, Some fixed point theorems of LeggettWilliams type,
Rocky Mountain Journal of Mathematics, 41:2 (2011) 371–386.

91. 
with Richard I. Avery, Johnny Henderson, and Xueyan Liu, Operator type expansioncompression fixed point theorem,
Electronic Journal of Differential Equations, 2011 (2011), No. 42, 1–11.

90. 
with Richard I. Avery, Existence of a periodic solution for continuous and discrete periodic secondorder equations with variable potentials,
Journal of Applied Mathematics and Computing, 37 (2011) 297–312.

89. 
with Richard I. Avery, Johnny Henderson, Xueyan Liu, and Jeff W. Lyons, Existence of a positive solution for a right focal discrete boundary value problem,
Journal of Difference Equations and Applications, 17:11 (2011) 1635–1642.

88. 
with Christopher C. Tisdell, Alternative solutions of inhomogeneous secondorder linear dynamic equations on time scales,
Journal of Difference Equations and Applications, 17:10 (2011) 1487–1498.

87. 
with Chengbo Zhai, A sum operator equation and applications to nonlinear elastic beam equations and LaneEmdenFowler equations,
Journal of Mathematical Analysis and Applications, 375:2 (2011) 388–400.

86. 
TitchmarshSimsWeyl theory for complex Hamiltonian systems on Sturmian time scales,
Journal of Mathematical Analysis and Applications, 373 (2011) 709–725.

85. 
with John R. Graef, SturmPicone comparison theorem for matrix systems on time scales,
Applicable Analysis and Discrete Mathematics, 4 (2010) 338–346.

84. 
with Agacik Zafer, Interval criteria for secondorder superhalflinear functional dynamic equations with delay and advance arguments,
Journal of Difference Equations and Applications, 16:8 (2010) 917–930.

83. 
with Richard I. Avery and Johnny Henderson, Functional expansion  compression fixed point theorem of LeggettWilliams type,
Electronic Journal of Differential Equations, Vol. 2010(2010) No. 63, pp. 1–9. 
82. 
with Richard I. Avery and Johnny Henderson, Existence of a positive solution to a right focal boundary value problem,
Electronic Journal of Qualitative Theory of Differential Equations, 2010 (2010) No. 5, 1–6.

81. 
with Ravi P. Agarwal and Agacik Zafer, Interval oscillation criteria for secondorder forced delay dynamic equations with mixed nonlinearities,
Computers & Mathematics with Applications, 59 (2010) 977–993.

80. 
with Chengbo Zhai, Positive solutions to semipositone secondorder threepoint problems on time scales,
Applied Mathematics and Computation, 215 (2010) 3713–3720.

79. 
with Richard I. Avery and Johnny Henderson, A topological proof and extension of the LeggettWilliams fixed point theorem,
Communications on Applied Nonlinear Analysis, 16:4 (2009) 39–44.

78. 
with Richard I. Avery, Green's function of a centered partial difference equation,
Electronic Journal of Qualitative Theory of Differential Equations, Spec. Ed. I, No 4. (2009) 1–12.

77. 
with Abdelkader Boucherif, Nonlocal initial value problem for firstorder dynamic equations on time scales,
Dynamics of Continuous, Discrete and Impulsive Systems (Series A) Math. Anal., 16 (2009), Differential Equations and Dynamical Systems, suppl. S1,
162–166.

76. 
with Feliz Minhós, Existence of solutions for a fourthorder multipoint beam problem on measure chains,
Electronic Journal of Differential Equations, 2009 (2009) No. 98, 1–10.

75. 
with Agacik Zafer, Nonlinear oscillation of secondorder dynamic equations on time scales,
Applied Mathematics Letters, 22 (2009) 1591–1597.

74. 
with Feliz Minhós, A discrete fourthorder Lidstone problem with parameters,
Applied Mathematics and Computation, 214 (2009) 523–533.

73. 
Oscillation and nonoscillation criteria for twodimensional timescale systems of firstorder nonlinear dynamic equations,
Electronic Journal of Differential Equations, 2009(2009) No. 24, 1–13.

72. 
with Patricia J.Y. Wong, Positive solutions for secondorder semipositone problems on time scales,
Computers & Mathematics with Applications, 58 (2009) 281–291.

71. 
Dominant and recessive solutions of selfadjoint matrix systems on time scales,
Nonlinear Dynamics and Systems Theory, 9:3 (2009) 219–238.

70. 
with George Smyrlis, Solvability for a thirdorder threepoint boundary value problem on time scales,
Mathematical and Computer Modelling, 49 (2009) 1994–2001.

69. 
with Jon Kwiatkowski '11, Asymptotic and oscillatory behavior of secondorder neutral quantum equations with maxima,
Electronic Journal of Qualitative Theory of Differential Equations, 2009(2009) No. 16, 1–9.

68. 
with Will Hall '11, Oscillation criteria for twodimensional systems of firstorder linear dynamic equations on time scales,
Involve, a Journal of Mathematics, 2:1 (2009) 1–16.

67. 
with Ilkay Yaslan Karaca,
Higherorder threepoint boundary value problem on time scales,
Computers & Mathematics with Applications, 56 (2008) 2429–2443.

66. 
Global stability for nonlinear dynamic equations with variable coefficients,
Journal of Mathematical Analysis and Applications, 345:2 (2008) 796–804.

65. 
Interval criteria for oscillation of nonlinear secondorder dynamic equations on time scales,
Nonlinear Analysis, 69 (2008) 4614–4623.

64. 
Existence of solutions for a firstorder pLaplacian bvp on time scales,
Nonlinear Analysis, 69 (2008) 4521–4525.

63. 
Global attractivity for nonlinear delay dynamic equations,
International Journal of Difference Equations, 3:1 (2008) 37–51.

62. 
Nonlinear dynamic integral inequalities in two independent variables on time scale pairs,
Advances in Dynamical Systems and Applications, 3:1 (2008) 1–13.

61. 
Existence of solutions for firstorder multipoint problems with changingsign nonlinearity,
Journal of Difference Equations and Applications, 14:6 (2008) 657–666.

60. 
Dynamic double integral inequalities in two independent variables on time scales,
Journal of Mathematical Inequalities, 2:2 (2008) 163–184.

59. 
with Jo Hoffacker,
Higherdimensional functional dynamic equations on periodic time scales,
Journal of Difference Equations and Applications, 14:1 (2008) 83–89.

58. 
Young's integral inequality on time scales revisited,
Journal of Inequalities in Pure and Applied Mathematics, Volume 8 (2007), Issue 3, Article 64, 5 pages.

57. 
with Jo Hoffacker,
Existence of solutions to a thirdorder multipoint problem on time scales,
Electronic Journal of Differential Equations, Vol. 2007(2007), No. 107, pp. 1–15.

56. 
with Zeqing Liu, Jeong Sheok Ume, and Shin Min Kang,
Twin monotone positive solutions to a singular nonlinear thirdorder differential equation,
Journal of Mathematical Analysis and Applications, 334 (2007) 299–313.

55. 
with Lisa Moats '10,
qDominant and qrecessive matrix solutions for linear quantum systems,
Electronic Journal of Qualitative Theory of Differential Equations, 2007 No. 11, 1–29.

54. 
Oscillation of secondorder forced functional dynamic equations with oscillatory potentials,
Journal of Difference Equations and Applications, 13:5 (2007) 407–421.

53. 
with Bobbi Buchholz,
Selfadjoint matrix equations on time scales,
PanAmerican Mathematical Journal, 17:2 (2007) 81–104.

52. 
with Irena Rachunková and Chris Tisdell,
Solvability of discrete Neumann boundary value problems,
Journal of Mathematical Analysis and Applications, 331 (2007) 736–741.

51. 
with Chris Tisdell,
Thirdorder nonlocal problems with signchanging nonlinearity on time scales,
Electronic Journal of Differential Equations, 2007 (2007), No. 19, 1–12.

50. 
with Zackary Kenz '08,
Global asymptotic behavior for delay dynamic equations,
Nonlinear Analysis, 66 (2007) 1633–1644.

49. 
Boundedness and vanishing of solutions for a forced delay dynamic equation,
Advances in Difference Equations, 2006 (2006), Article ID 35063, 17 pages.

48. 
Secondorder npoint problems on time scales with changingsign nonlinearity,
Advances in Dynamical Systems and Applications, 1:1 (2006) 17–27.

47. 
with Alberto Cabada,
Thirdorder rightfocal multipoint problems on time scales,
Journal of Difference Equations and Applications, 12:9 (2006) 919–935.

46. 
with Joan Hoffacker,
Existence of solutions for a cantilever beam problem,
Journal of Mathematical Analysis and Applications, 323 (2006) 958–973.

45. 
Asymptotic behavior of solutions for neutral delay dynamic equations on time scales,
Advances in Difference Equations, 2006:80850 (2006) 1–11.

44. 
with Ruyun Ma,
Secondorder npoint eigenvalue problems on time scales,
Advances in Difference Equations, 2006:59572 (2006) 1–17.

43. 
with Gusein Guseinov and Jo Hoffacker,
Higherorder self adjoint boundary value problems on time scales,
Journal of Computational and Applied Mathematics 194:2 (2006) 309–342.

42. 
with Richard Avery,
A fourthorder fourpoint rightfocal boundary value problem,
Rocky Mountain Journal of Mathematics 36:2 (2006) 367–380.

41. 
with Robert Krueger and Allan Peterson,
Delay dynamic equations with stability,
Advances in Difference Equations 2006:94051 (2006) 1–19.

40. 
with Joan Hoffacker,
Positive periodic timescale solutions for functional dynamic equations,
Australian Journal of Mathematical Analysis and Applications 3:1:5 (2006) 1–14.

39. 
with Tyler O. Anderson '06 and Mathew M. Kleber '06,
Green's function and existence of solutions for a functional focal differential equation,
Electronic Journal of Differential Equations 2006:12 (2006) 1–14.

38. 
with Richard Avery and Robert Krueger,
An extension of the fixed point theorem of cone expansion and compression of functional type,
Communications on Applied Nonlinear Analysis 13:1 (2006) 15–26.

37. 
Existence of solutions for nonlinear multipoint problems on time scales,
Dynamic Systems and Applications 15 (2006) 21–34.

36. 
with Nicholas Myran '05 and Dustin White '05,
Basins of attraction in a Cournot duopoly model of Kopel,
Journal of Difference Equations and Applications 11:10 (2005) 879–887.

35. 
Timescale integral inequalities,
Journal of Inequalities in Pure and Applied Mathematics 6:3:66 (2005) 1–17.

34. 
Eigenvalue intervals for evenorder SturmLiouville dynamic equations,
Communications on Applied Nonlinear Analysis 12:4 (2005) 1–13.

33. 
with Joan Hoffacker,
Evenorder selfadjoint timescale problems,
Electronic Journal of Differential Equations 2005:24 (2005) 1–9.

32. 
Multiple periodic solutions for a secondorder problem on periodic time scales,
Nonlinear Analysis TMA 60:1 (2005) 101–115.

31. 
Twin npoint boundary value problems,
Applied Mathematics Letters 17:9 (2004) 1053–1059.

30. 
with Richard Avery and Johnny Henderson,
Existence of solutions for a onedimensional pLaplacian on time scales,
Journal of Difference Equations and Applications 10:10 (2004) 889–896.

29. 
Nonlinear triplepoint problems on time scales,
Electronic Journal of Differential Equations 2004:47 (2004) 1–12.

28. 
with Richard Avery,
An evenorder threepoint boundary value problem on time scales,
Journal of Mathematical Analysis and Applications 291:2 (2004) 514–525.

27. 
Extension of a secondorder multipoint problem to time scales,
Dynamic Systems and Applications 12:3–4 (2003) 393–404.

26. 
with Joan Hoffacker,
A stacked deltanabla selfadjoint problem of even order,
Mathematical and Computer Modelling 38 (2003) 481–494.

25. 
Kamenevtype oscillation criteria for linear Hamiltonian systems,
PanAmerican Mathematical Journal 13:4 (2003) 71–75.

24. 
Green's function for a thirdorder generalized right focal problem,
Journal of Mathematical Analysis and Applications 288:1 (2003) 1–14.

23. 
Discrete thirdorder threepoint right focal boundary value problems,
Computers & Mathematics with Applications 45 (2003) 861–871.

22. 
with Richard Avery and John Davis,
Existence and uniqueness of solutions to discrete diffusion equations,
Computers & Mathematics with Applications 45 (2003) 1075–1085.

21. 
Existence of a solution to a higherorder discrete threepoint problem,
Electronic Journal of Differential Equations 2003:40 (2003) 1–7.

20. 
with John Bullock '02, Lynn Erbe, Allan Peterson, and Hoi Nam Tran,
Nabla dynamic equations on time scales,
PanAmerican Mathematical Journal 13:1 (2003) 1–47.

19. 
with Joan Hoffacker,
Green's function for an evenorder mixed derivative problem on time scales,
Dynamic Systems and Applications 12:1–2 (2003) 9–22.

18. 
A fourthorder nonlinear difference equation,
Journal of Difference Equations and Applications 9:1 (2003) 161–169.

17. 
Taylor polynomials for nabla dynamic equations on time scales,
PanAmerican Mathematical Journal 12:4 (2002) 17–27.

16. 
with Richard Avery,
Fixed point theorem of cone expansion and compression of functional type,
Journal of Difference Equations and Applications 8:11 (2002) 1073–1083.

15. 
Eigenvalue intervals for a secondorder mixedconditions problem on time scales,
International Journal of Nonlinear Differential Equations 7:1–2 (2002) 97–104.

14. 
Solutions to secondorder threepoint problems on time scales,
Journal of Difference Equations and Applications 8:8 (2002) 673–688.

13. 
with John Davis,
Multiple solutions and eigenvalues for a thirdorder right focal boundary value problem,
Journal of Mathematical Analysis and Applications 267:1 (2002) 135–157.

12. 
with Richard Avery,
Existence of three positive solutions to a secondorder boundary value problem on a measure chain,
Journal of Computational and Applied Mathematics 141: 1–2 (2002) 65–73.

11. 
Eigenvalue intervals for a twopoint boundary value problem on a measure chain,
Journal of Computational and Applied Mathematics 141:1–2 (2002) 57–64.

10. 
with Richard Avery and Johnny Henderson,
Corollary to the five functionals fixed point theorem,
Journal of Nonlinear Studies 8:4 (2001) 451–464.

9. 
with Richard Avery,
Multiple positive solutions to a third order discrete focal boundary value problem,
Computers & Mathematics with Applications 42 (2001) 333–340.

8. 
with Allan Peterson,
Asymptotic properties of solutions of a 2norder differential equation on a time scale,
Mathematical and Computer Modelling 32 (2000) 653–660.

7. 
Positivity of Green's function for an npoint right focal boundary value problem on measure chains,
Mathematical and Computer Modelling 31 (2000) 29–50.

6. 
Normalized prepared bases for discrete symplectic matrix systems,
Dynamic Systems and Applications 8 (1999) 335–344.

5. 
A 2nthorder linear difference equation,
Communications in Applied Analysis 2:4 (1998) 521–529.

4. 
Multiple positive solutions for a threepoint boundary value problem,
Mathematical and Computer Modelling 27:6 (1998) 49–57.

3. 
Green's function for an npoint discrete right focal boundary value problem,
PanAmerican Mathematical Journal 8:2 (1998) 45–70.

2. 
with Richard Avery and Allan Peterson,
Three positive solutions to a discrete focal boundary value problem,
Journal of Computational and Applied Mathematics 88:1 (1998) 103–118.

1. 
Discrete trigonometric matrix functions,
PanAmerican Mathematical Journal 7:1 (1997) 39–54.


