Recent Publications of Allan Peterson

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176 With J. Baoguo, C. Goodrich, and L. Erbe, The relation between nabla fractional differences and nabla integer differences, in progress
175 With J. Baoguo and L. Erbe, Some relations between the Caputo fractional difference operators and integer order differences, Submitted 2014
174 With J. Baoguo and L. Erbe, Convexity for nabla and delta fractional differences, Journal of Difference Equations and Applications, to appear.
173 With S. H. Saker and R. R. Mahmoud, A unified approach to Copson and Beesack type inequalities on time scales, submited
172 172. With J. Baoguo and L. Erbe, Two monotonicity results for nabla and delta fractional differences, Submitted 2014.
171 With S. H. Saker and R. R. Mahmoud, Some Bennett-Copson type inequalities on time scales, submitted 2014.
170 With S. H. Saker and R. R. Mahmoud, Weighted Hardy's inequality on time scales, Mediterranean Journal of Mathematics, accepted December 2014.
169 With P. Awasthi and L.Erbe, Existence and uniqueness results for positive solutions of a nonlinear fractional difference equation, Communications in Applied Analysis, to appear.
168 With A. Feza G\"{u}venilir, Billur Kaymak\c{c}alan, and Kenan\ Ta\c{s}, Nabla Discrete Fractional Grüss Type Inequality, J. Inequalities Applcations, 2014.
167 With J. Baoguo and L. Erbe, A Butler-type oscillation theorem for second order dynamic equations on discrete time scales, JDEA, 20 (2014) 671-684.
166 With L. Erbe and R. Mert, Spectral parameter power series for Sturm—Liouville problems, Applied Mathematics and Computation, 218 (2012) 7671-7678.
165 With L. Erbe , R. Mert, and A. Zafer, Oscillation of even order nonlinear delay dynamic equations on time scales, Czechoslovak Math. J., 63 (138) (2013) 265—279.
164 With J. Baoguo and L. Erbe, Oscillation theorems for second order sublinear dynamic equations on time scales, Dynam. Cont., Discrete, Impulsive Syst. Series A: Math. Anal. 19 (2012) 615—626.
163 With L. Erbe and G. Hovhannisyan, Hovhannisyan, Wiman's formula for a second order dynamic equation , Advances in Difference Equations, to appear.
162 With J. Baoguo and L. Erbe, An oscillation theorem for second order superlinear dynamic equations on time scales, Applied Math. Comput., 219 (2013) 10333—10342.
161 With R. Dahal, L. Erbe and R. Higgins, Guest Editors, Communications Appl. Anal., 16 (2012) 203 pages.
160 With L. Erbe, Dynamic Equations on Time Scales and Applications, Foreword, Int. J. Dynamic Systems Diff. Equs, 3 (1/2) (2011) 1-2.
159 With L. Erbe and G. Hovhannisyan, Oscillation theorems for n-th order dynamic equations on a time scale, Nonlinear Dynamics and Systems Theory, 12(1) (2012) 63—80.
158 With J. Baoguo and L. Erbe, Oscillation of n-th order linear dynamic equations on time scales, Communications Appl. Anal. 16 (3) (2012) 447-458.
157 With J. Baoguo and L. Erbe, Asymptotic Behavior of n-th Order Sublinear Dynamic Equations on Time Scales, Communications in Applied Analysis, 15 (2011) 183-194.
156 With L. Erbe, Lloyd K. Jackson's life and work, Rocky Mountain J. Math., 41 (2) (2011) 1-4.
155 With L. Erbe and J. Baoguo, Oscillation of n-th order superlinear dynamic equations on time scales, Rocky Mountain J. Math. 41 (2) (2011) 471—491.
154 With L. Erbe, Editors, Dynamic Equations on Time Scales with Applications, : International J. Dynam. Systems Appl., 3 (1/2) (2011) (287 pages).
153 With Walter Kelley, The Theory of Differential Equations: Classical and Qualitative, Second Edition, Springer 2010.
152 With L. Erbe and B. Karpuz, Kamenev-type oscillation criteria for higher-order neutral delay, International J. Difference Equations, 6 (2011) 1-16.
151 With L. Erbe and J. Baoguo, On the Asymptotic behavior of solutions of Emden-Fowler equations on time scales, Annali de Matematica Pura ed Applicata, 191 (2) (2012) 205—217.
150 With L. Erbe and T. S. Hassan, Oscillation of second order functional dynamic equations, Internat. J. Difference equs., 5 (2) (2010) 353—371.
149 With L. Erbe and T. S. Hassan, Oscillation criteria for first order dynamic equations, Appl. Anal. Disc. Math., 3 (2009) 253-263.
148 With L. Erbe and T. S. Hassan, Oscillation criteria for second order sublinear dynamic equations with damping term, J. Difference Equs. Appl., 17 (4) (2011) 505-523.
147 With L. Erbe and T. S. Hassan, Oscillation of third order functional dynamic equations with mixed arguments on time scales, J. Appl. Math. Comput., 34 (2010) 61-73.
146 With T. S. Hassan and L. Erbe, Oscillation of second order superlinear dynamic equations with damping on time scales, Comp. Math. Appl., 59 (2010) 550--558.
145 With L. Erbe and T. S. Hassan, Oscillation criteria for forced second order functional dynamic equations on time scales with mixed nonlinearities, Advances Dynam. Syst. Appl., 5 (2010) 61-73.
144 With J. Baoguo and L. Erbe, Belohorec-type oscillation theorem for second order sublinear dynamic equations on time scales, Mathematische Nachrichten, 284(13) (2011) 1658-1668.
143 J. Baoguo and L. Erbe, Kiguradze-type oscillation theorems for second order superlinear dynamic equations on time scales, Canad. Math. Bull., 54(4) (2011) 580-592.
142 J. Baoguo and L. Erbe, Nonoscillation for a second order sublinear Emden--Fowler dynamic equation on a time scale, J. Computation Appl. Math., 232 (2009) 594--599.
141 J. Baoguo and L. Erbe, Oscillation of sublinear Emden-Fowler dynamic equations on a time scale, Journal Difference Equations Applications, 16 (2010) 217--226.
140 L. Erbe and T. S. Hassan, Forced oscillation of second order delay differential equations with mixed nonlinearities, Acta Matematica Scientia, 31 Ser B (2) (2010) 613-626.
139 L. Erbe, T. Hassan and S. H. Saker, Interval oscillation criterion for forced second-order nonlinear delay dynamic equations with oscillatory potential, DCDIS, Series A, 17 (2010) 533—542.
138 L. Erbe and T. Hassan, Oscillation of third order nonlinear functional dynamic equations on time scales, Differential Equations and Dynamical Systems, 18 (2010) 199-227.
137 J. Baoguo and L. Erbe, Oscillation of a family of q-difference equations, Appl. Math. Letters., 22 (2009) 871-875.
136 L. Erbe and T. Hassan, Oscillation criteria for nonlinear functional neutral dynamic equations on time scales, J. Difference Equations Appl., 15 (2009) 1097-1116.
135 J. Baoguo and Lynn Erbe, Oscillation and nonoscillation of second order linear dynamic equations with integrable coefficients on time scales, Appl. Math. Comput., 215 (2009) 1868-1885.
134 J. Baoguo and Lynn Erbe, A Wong-type oscillation theorem for second order linear dynamic equations, J. Difference Equ. Appl., 16 (2010) 1097-1116.
133 With L. Erbe and T. Hassan, Oscillation criteria for nonlinear damped dynamic equations on time scales, Appl. Math. Comput., 203 (2008) 343-357.
132 With M. Bohner and I. Gyori, in progress
131 J. Baoguo and Lynn Erbe, New comparison and oscillation results for second order half-linear dynamic equations on time scales, Comput. Math. Appl. 56 (2008) 2744-2756.
130 J. Baoguo and Lynn Erbe, Some new comparison results for second order linear dynamic Equations, Canad. Appl. Quart., 15 (2007) 349-366.
129 L. Erbe, T. Hassan, and S. H. Saker, Oscillation criteria for sublinear half--linear delay equations, Internat. J. Difference Equs., 3 (2008) 227--245.
128 With L. Erbe, T. Hassan, and S. H. Saker, Oscillation Criteria for half--linear delay dynamic equations, Nonlin. Dynam. Syst. Thy., 9 (2009) 51--68.
127 With L. Erbe and T. S. Hassan, Oscillation of second order neutral delay differential equations, Advances Dynam. Systems Appl., 3 (2008) 73--88.
126 With L. Erbe and J. Weiss, Positive solutions to a singular second order boundary value problem, Advances Dynam. Syst. Appl., 3 (2008) 89--105.
125 With L. Erbe, A. Ruffing, and A. Suhrer, Numerical results for Schrodinger difference equations, Internat. J. Difference Equations, 3 (2008) 247--266.
124 With M. Bohner, Quest Editors, Internat. J. Difference Equs., 2007.
123 With L. Erbe and C. C. Tisdell, Basic existence, uniqueness and approximation results for positive solutions to nonlinear dynamic equations on time scales, J. Nonlinear Analysis Series A: Theory, Methods, Appl., 69 (2008) 2303-2317.
122 With L. Erbe and S. H. Saker, Oscillation criteria for a forced second-order dynamic equation, JDEA, 14 (2008) 997--1009.
121 With L. Erbe , Some oscillation results for second order linear delay dynamic equations, Advanced Studies in Pure Math, Advances in Discrete Systems, 53 (2009) 215--223.
120 With L. Erbe and S. H. Saker, Oscillation criteria for second-order nonlinear delay dynamic equations, J. Math. Anal. Appl., 333 (2007) 505--522.
119 With L. Erbe and S. H. Saker, Hille and Nehari type criteria for third-order dynamic equations, J. Math. Anal. Appl., 329 (2007) 112--131.
118 With L. Erbe and S. H. Saker, Hille-Kneser type criteria for second-order dynamic equations on time scales, Advances Difference Equ., 2006 (2006)
117 With L. Erbe and S. H. Saker, Oscillation and asyptotic behavior of a third order nonlinear dynamic equation on a time scale, Canad. Quart. Appl. Math., 14 (2006) 129--146.
116 With L. Erbe and Pavel Rehak, Integral comparison theorems for second order linear dynamic equations, Proceedings of the International Conference, Difference Equations, Special Functions, and Orthogonal Polynomials, World Scientific Publ., Singapore 2007 497--506.
115 With M. Bohner, Guest Editors, Dynamic Equations on Time Scales and Applications, Advances Difference Equ., 2006 (2006).
114 With D. Anderson and R. Krueger, Delay dynamic equations with stability, Advances Difference Equ., 2006 (2006) 1--19.
113 With Bevan Thompson, The Henstock-Kurzweil delta and nabla integrals, J. Math. Anal. Appl., 323 (2006) 162--178.
112 With L. Erbe and S.H. Saker, Kamenev-type oscillation criteria for second-order linear delay dynamic equations, Dynam. Sys. Appl., 15 (2006) 65--78.
111 With L. Erbe and C. C. Tisdell, Monotone Solutions of Dynamic Systems on Time Scales, J. Difference Equ. Appl., 12 (2006) 343--355.
110 With L. Erbe, Comparison Theorems of Hille-Wintner Type for Dynamic Equations on Time Scales, Proc. Amer. Math. Soc., 133 (2005) 3243--3253.
109 With M. Bohner and L. Erbe, Oscillation for nonlinear second order dynamic equations on a time scale, J. Math. Anal. Appl., 301 (2005) 491--507.
108 With Y. Raffoul, Exponential Stability of dynamic equations on time scales, Boundary Value Problems, Advances Difference Equ., 2005:2 (2005) 133--144.
107 With L. Erbe and C.C. Tisdell, Existence of solutions to second-order BVPs on time scales, Applicable Anal., 84:10 (2005) 1069--1078.
106 With L. Erbe, Some recent results in linear and nonlinear oscillation, Proc. ICDSA, May 2003, Atlanta, Dynam. Sys. Appl., 13 (2004), 381--395.
105 With L. Erbe, An oscillation result for a nonlinear dynamic equation on a time scale, Canad. Quart. Appl. Math., 11 (2003) 143--157.
104 With L. Erbe and S.H. Saker, Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales, J. Comput. Appl. Math., 181 (2005) 92--102.
103 With L. Erbe and M. Simon, Square integrability of Gaussian bells on time scales, Comput. Math. Appl., 49 (2005) 871--883.
102 With J. Henderson and C. Tisdell, On the existence and uniqueness of solutions to boundary value problems on time scales, Advances Difference Equ., 2004 (2004) 93--109.
101 With C. Tisdell and Y. Raffoul, Three point boundary value problems on time scales, J. Difference Equ. Appl., 10 (2004) 843--849.
100 With Chris Tisdell, Boundedness and Uniqueness of Solutions to Dynamic Equations on Time Scales, J. Difference Equ. Appl., 10 (2004) 1295--1306.
99 With Lynn Erbe, Recent results concerning dynamic equations on time scales, Proc. 2002 Bexbach Conference, Electron. Trans. Numerical Anal., to appear 2007.
98 With M. Bohner and G. Guseinov, Wrote Chapter 1 of the book, Advances in Dynamic Equations on Time Scales, Birkhauser, 2003, 1--15.
97 With S. Huff, G. Olumolade, N. Pennington, Oscillation of an Euler-Cauchy dynamic equation, Proceedings of the fourth international conference on dynamical systems and differential equations, Discrete Cont. Dynam. Sys., (2002) 24--27.
96 With L. Erbe, Boundedness and oscillation for nonlinear dynamic equations on a time scale, Proc. Amer. Math. Soc., 132 (2003) 735--744.
95 With L. Erbe and S. H. Saker, Oscillation criteria for second-order nonlinear dynamic equation on time scales, J. London Math. Soc., 67 (2003) 701--714.
94 With L. Erbe and P. Rehak, Comparison theorems for linear dynamic equations on time scales, J. Math. Analysis Appl., 275 (2002) 418--438.
93 With Walter Kelley, The Theory of Differential Equations: Classical and Qualitative, Prentice Hall, 2004.
92 With Martin Bohner, Editors, Advances in Dynamic Equations on Time Scales, Birkhauser, 2003.
91 Preface: Dedication to L. Erbe, J. Difference Equ. Appl., 8 (2002) 293--294.
90 With D. Anderson, J. Bullock, L. Erbe, and H. Tran, Nabla dynamic equations on time scales, (see also Chapter 3 of book, Advances in Dynamic Equations on Time Scales, Birkhauser, 2002), PanAmer. Math. J., 13 (2003) 1--47.
89 With R. Higgins, Cauchy functions and Taylor’s formula for time scales, Proceedings of the 6th ICDEA in Augsburg, Germany, 2001, new Progress in Difference Equations, Edited by B. Aulbach, S. Elaydi, and G. Ladas, J. Difference Equ. Appl., (2003) 299--308.
88 With E. Akin, M Bohner, and L. Erbe, Existence of bounded solutions for second order dynamic equations, J. Difference Equ. Appl., 8 (2002), 389--401.
87 87. Journal of Difference Equations and Applications, Guest Editor, 7 (2001).
86 Preface: Dedication to Calvin Ahlbrandt, J. Difference Equ. Appl., 7 (2001) 763--766.
85 With R.P. Agarwal and M. Bohner, Inequalities on time scales, a survey, Math. Inequa. Appl., 4 (2001) 535--557.
84 With M. Bohner, Dynamic Equations on Time Scales, Birhauser, Boston, 2001.
83 With L. Erbe, Averaging techniques for self-adjoint matrix equations on a measure chain, J. Math. Anal. Appl., 271 (2002) 31--58.
82 With E. Akin, L. Erbe, and B. Kaymakalan, Oscillation results for a dynamic equation on a time scale, J. Meth. Appl. Anal., 7 (2001) 793--810.
81 With M. Bohner, Laplace transform and z-transform: Unification and extension, Methods Appl. Anal., 9 (2002) 151--158. (See also ULMER SEMINARE 2001, Funktionalanalysis and Differentialgleichumgen, Heft 6, 69--75).
80 With R. Agarwal, M. Bohner, and D. O'Regan, Dynamic equations on time scales: A survey, J. Comput. Appl. Math., 141 (2002) 1--26. (See also ULMER SEMINARE 2000, Funktionalanalysis and Differentialgleichumgen, Heft, 5 (2000) 1--35).
79 With M. Bohner, First and second order linear dynamic equations on time scales, J. Difference Equ. Appl., 7 (2001) 767--792.
78 With M. Bohner, A Survey of exponential functions on time scales, Rev. Cubo Matematica Educacimal, 3 (2001) 285--301.
77 With W. Kelley, Difference Equations: An Introduction with Applications, Academic Press, Second Edition, 2001.
76 With L. Erbe, Oscillation criteria for second order matrix dynamic equations on a time scale. Journal of Computational and Applied Mathematics, 141 (2002) 169--186.
75 With R. Avery, Three positive fixed points of nonlinear operators on ordered Banach spaces, Comput. Math. Appl., 42 (2001) 313--322.
74 With L. Erbe, Riccati equations on a measure chain, Dynamical Systems and Applications, Proc. Dynam. Sys.Appl., 3 (2001) 193--200.
73 With L. Erbe and R. Mathsen, Existence, multiplicity, and nonexistence of positive solutions to a differential equation on a measure chain, J. Comput. Appl. Math., 113 (2000) 365--380.
72 With L. Erbe and R. Mathsen, Factoring linear differential operations on measure chains, J. Inequal. Appl., 6 (2001) 287--303.
71 With L. Erbe, Eigenvalue conditions and positive solutions, Journal of Difference Equations and Applications, J. Difference Equ. Appl., 6 (2000) 165--191.
70 With M. Morelli, A third order differential equation on a time scale, Math. Comput. Modeling, 32 (2000) 565--570.
69 With D. Anderson, Asymptotic properties of solutions of a 2n-th order differential equation on a time scale, Mathematical and Computer Modeling, 32 (2000) 653--660
68 With C. Ahlbrandt, R. Agarwal, and M. Bohner, Discrete linear Hamiltonian systems: a survey, Dynam. Sys. Appl., 8 (1999) 307--333.
67 With L. Erbe, (Preface: Dedication to Lloyd Jackson), Boundary Value Problems and Related Topics, Edited by L. Erbe and A. Peterson, Math. Comput. Modeling, 32 (2000) xiii--xiv.
66 With L. Erbe, Boundary Value Problems and Related Topics, Math. Comput. Modeling, Guest Editors, 32 (2000).
65 With L. Erbe, Positive solutions for a nonlinear differential equation on a measure chain, Math. Comput. Modeling, 32 (2000) 571--585.
64 With L. Erbe, Green's functions and comparison theorems for differential equations on measure chains, Dynamics of Continuous , Discrete Impul. Sys., 6 (1999) 121--137.