Allan C. Peterson

Personal Home Page

http://mobius.unl.edu/~apeterson1/

Articles in Scholarly Journals [Incomplete List]

  1. Basic existence, uniqueness and approximation results for positive solutions to nonlinear dynamic equations on time scales
    Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 7, pp. 2303–2317, 2008
  2. Hille and Nehari type criteria for third-order dynamic equations
    Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 112–131, 2007
  3. Oscillation criteria for second-order nonlinear delay dynamic equations
    Journal of Mathematical Analysis and Applications, vol. 333, no. 1, pp. 505–522, 2007
  4. Monotone solutions of dynamic systems on time scales
    The Journal of Difference Equations and Applications, vol. 12, no. 3-4, pp. 343–355, 2006
  5. Henstock–Kurzweil delta and nabla integrals?
    Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 162–178, 2006
  6. Hille-Kneser-type criteria for second-order dynamic equations on time scales
    Advances in Difference Equations, vol. 2006, Article ID 51401, 18 pages, 2006
  7. Dynamic equations and applications
    Advances in Difference Equations, vol. 2006, Article ID 83968, 1 pages, 2006
  8. Delay dynamic equations with stability
    Advances in Difference Equations, vol. 2006, Article ID 94051, 19 pages, 2006
  9. Proceedings of the American Mathematical Society, vol. 133, no. 11, pp. 3243–3254, 2005
  10. Exponential stability of dynamic equations on time scales
    Advances in Difference Equations, vol. 2005, no. 2, pp. 133–144, 2005
  11. Existence of solutions to second-order BVPs on time scales
    Applicable Analysis, vol. 84, no. 10, pp. 1069–1078, 2005
  12. Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales
    Journal of Computational and Applied Mathematics, vol. 181, no. 1, pp. 92–102, 2005
  13. Square integrability of Gaussian bells on time scales
    Computers & Mathematics with Applications, vol. 49, no. 5-6, pp. 871–883, 2005
  14. Oscillation for nonlinear second order dynamic equations on a time scale
    Journal of Mathematical Analysis and Applications, vol. 301, no. 2, pp. 491–507, 2005
  15. On the existence and uniqueness of solutions to boundary value problems on time scales
    Advances in Difference Equations, vol. 2004, no. 2, pp. 93–109, 2004
  16. Proceedings of the American Mathematical Society, vol. 132, no. 03, pp. 735–745, 2004
  17. Boundedness and Uniqueness of Solutions to Dynamic Equations on Time Scales
    The Journal of Difference Equations and Applications, vol. 10, no. 13-15, pp. 1295–1306, 2004
  18. Three Point Boundary Value Problems on Time Scales
    The Journal of Difference Equations and Applications, vol. 10, no. 9, pp. 843–849, 2004
  19. Oscillation Criteria for Second-Order Nonlinear Dynamic Equations On Time Scales
    Journal of the London Mathematical Society, vol. 67, no. 3, pp. 701–714, 2003
  20. Existence of Bounded Solutions for Second Order Dynamic Equations
    The Journal of Difference Equations and Applications, vol. 8, no. 4, pp. 389–401, 2002
  21. Dedication to Professor Allan Peterson
    The Journal of Difference Equations and Applications, vol. 8, no. 9, pp. 761–764, 2002
  22. Dedication to Lynn Erbe
    The Journal of Difference Equations and Applications, vol. 8, no. 4, pp. 293–294, 2002
  23. Averaging techniques for self-adjoint matrix equations on a measure chain
    Journal of Mathematical Analysis and Applications, vol. 271, no. 1, pp. 31–58, 2002
  24. Comparison theorems for linear dynamic equations on time scales
    Journal of Mathematical Analysis and Applications, vol. 275, no. 1, pp. 418–438, 2002
  25. Dynamic equations on time scales: a survey
    Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 1–26, 2002
  26. Oscillation criteria for second-order matrix dynamic equations on a time scale
    Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 169–185, 2002
  27. First and second order linear dynamic equations on time scales
    Journal of Difference Equations and Applications, vol. 7, no. 6, pp. 767–792, 2001
  28. Oscillation results for a dynamic equation on a time scale
    Journal of Difference Equations and Applications, vol. 7, no. 6, pp. 793–810, 2001
  29. Three positive fixed points of nonlinear operators on ordered banach spaces
    Computers & Mathematics with Applications, vol. 42, no. 3-5, pp. 313–322, 2001
  30. Eigenvalue conditions and positive solutions
    Journal of Difference Equations and Applications, vol. 6, no. 2, pp. 165–191, 2000
  31. Existence, multiplicity, and nonexistence of positive solutions to a differential equation on a measure chain
    Journal of Computational and Applied Mathematics, vol. 113, no. 1-2, pp. 365–380, 2000
  32. A third-order differential equation on a time scale
    Mathematical and Computer Modelling, vol. 32, no. 5-6, pp. 565–570, 2000
  33. Positive solutions for a nonlinear differential equation on a measure chain
    Mathematical and Computer Modelling, vol. 32, no. 5-6, pp. 571–585, 2000
  34. Asymptotic properties of solutions of a 2nth-order differential equation on a time scale
    Mathematical and Computer Modelling, vol. 32, no. 5-6, pp. 653–660, 2000
  35. Factoring linear differential operators on measure chains
    Journal of Inequalities and Applications, vol. 6, no. 3, pp. 287–303, 2000
  36. A quadratic functional for a third order linear difference equation
    Journal of Difference Equations and Applications, vol. 3, no. 5, pp. 463–472, 1998
  37. Three positive solutions to a discrete focal boundary value problem
    Journal of Computational and Applied Mathematics, vol. 88, no. 1, pp. 103–118, 1998
  38. Bounds for positive solutions for a focal boundary value problem
    Computers & Mathematics with Applications, vol. 36, no. 10-12, pp. 99–107, 1998
  39. Boundary value problems for functional difference equations
    Applied Mathematics Letters, vol. 9, no. 3, pp. 57–61, 1996
  40. The (2,2)-disconjugacy of a fourth order difference equation
    Journal of Difference Equations and Applications, vol. 1, no. 1, pp. 87–93, 1995
  41. The (n, n)-disconjugacy of a 2nth order linear difference equation
    Computers & Mathematics with Applications, vol. 28, no. 1-3, pp. 1–9, 1994
  42. Disconjugacy for a third order linear difference equation
    Computers & Mathematics with Applications, vol. 28, no. 1-3, pp. 131–139, 1994
  43. C-Disfocality for Linear Hamiltonian Difference Systems
    Journal of Differential Equations, vol. 110, no. 1, pp. 53–66, 1994
  44. Criteria for C-Disfocality of a Self-Adjoint Vector Difference Equation
    Journal of Mathematical Analysis and Applications, vol. 179, no. 2, pp. 512–524, 1993
  45. A Disconjugacy Criterion of W. T. Reid for Difference Equations
    Proceedings of the American Mathematical Society, vol. 114, no. 2, p. 459, 1992
  46. Atkinson’s Superlinear Oscillation Theorem for Matrix Difference Equations
    SIAM Journal on Mathematical Analysis, vol. 22, no. 3, p. 774, 1991
  47. Oscillation of second order linear matrix difference equations
    Journal of Differential Equations, vol. 89, no. 1, pp. 69–88, 1991
  48. A positivity result applied to difference equations
    Journal of Approximation Theory, vol. 59, no. 1, pp. 76–86, 1989
  49. A classification of the solutions of a difference equation according to their behavior at infinity
    Journal of Mathematical Analysis and Applications, vol. 136, no. 1, pp. 249–266, 1988
  50. Comparison Theorems for Eigenvalue Problems for nth Order Differential Equations
    Proceedings of the American Mathematical Society, vol. 104, no. 4, p. 1204, 1988
  51. Green's functions for (k, n ? k)-boundary value problems for linear difference equations
    Journal of Mathematical Analysis and Applications, vol. 124, no. 1, pp. 127–138, 1987
  52. Existence and uniqueness theorems for nonlinear difference equations
    Journal of Mathematical Analysis and Applications, vol. 125, no. 1, pp. 185–191, 1987
  53. Boundary Value Problems for an $n$th Order Linear Difference Equation
    SIAM Journal on Mathematical Analysis, vol. 15, no. 1, p. 124, 1984
  54. Existence–Uniqueness for Focal-Point Boundary Value Problems
    SIAM Journal on Mathematical Analysis, vol. 12, no. 2, p. 173, 1981
  55. Focal Green's functions for fourth-order differential equations
    Journal of Mathematical Analysis and Applications, vol. 75, no. 2, pp. 602–610, 1980
  56. Existence-uniqueness for ordinary differential equations
    Journal of Mathematical Analysis and Applications, vol. 64, no. 1, pp. 166–172, 1978
  57. Comparison theorems and existence theorems for ordinary differential equations
    Journal of Mathematical Analysis and Applications, vol. 55, no. 3, pp. 773–784, 1976
  58. On the sign of Green's functions
    Journal of Differential Equations, vol. 21, no. 1, pp. 167–178, 1976
  59. An Expression for the First Conjugate Point for an nth Order Nonlinear Differential Equation
    Proceedings of the American Mathematical Society, vol. 61, no. 2, p. 300, 1976
  60. Comparison theorems for boundary value problems
    Journal of Mathematical Analysis and Applications, vol. 52, no. 3, pp. 573–582, 1975
  61. A Theorem of Aliev
    Proceedings of the American Mathematical Society, vol. 23, no. 2, p. 364, 1969