Edit Profile (opens in new tab) Peterson, Allan C. Compute Distance To: Compute Author ID: peterson.allan-c Published as: Peterson, Allan; Peterson, Allan C.; Peterson, A.; Peterson, A. C.; Peterson, Alan more...less Homepage: https://www.math.unl.edu/~apeterson1/ External Links: MGP Documents Indexed: 174 Publications since 1969, including 6 Books 4 Contributions as Editor · 1 Further Contribution Co-Authors: 53 Co-Authors with 149 Joint Publications 2,469 Co-Co-Authors all top 5 Co-Authors 26 single-authored 85 Erbe, Lynn Harry 21 Jia, Baoguo 14 Baoguo, Jia 14 Saker, Samir H. 11 Bohner, Martin J. 9 Hassan, Taher S. 7 Hankerson, Darrel R. 7 Ridenhour, Jerry R. 6 Tisdell, Christopher C. 5 Anderson, Douglas Robert 5 Goodrich, Christopher S. 5 Mert, Raziye 4 Ahlbrandt, Calvin D. 4 Du, Feifei 4 Liu, Xiang 4 Mahmoud, Ramy Ramadan 3 Agarwal, Ravi P. 3 Avery, Richard I. 3 Henderson, Johnny Lee 3 Kelley, Walter G. 3 Peil, Timothy 3 Wu, Hongwu 2 Abdeljawad, Thabet 2 Akin, Elvan 2 Elaydi, Saber Nasr 2 Hu, Wei 2 Kaymakçalan, Billur 2 Mathsen, Ronald M. 2 Merdivenci Atici, Ferhan 2 Oganesyan, Gro R. 2 Raffoul, Youssef Naim 2 Řehák, Pavel 2 Schneider, John B. 1 Babuška, Ivo 1 Bullock, John D. 1 Burchett, B. 1 Chen, Churong 1 Chen, Siyuan 1 Ciarlet, Philippe Gaston 1 Diaz, Jerry 1 Eloe, Paul W. 1 Gallagher, Richard Hugo 1 Gensler, Scott 1 Graef, John R. 1 Gritsenko, Valeriĭ Alekseevich 1 Güvenilir, Ayşe Feza 1 Higgins, Raegan J. 1 Huff, S. 1 Krueger, Robert J. 1 Ladas, Gerasimos E. 1 Oden, John Tinsley 1 Olumolode, G. 1 O’Regan, Donal 1 Pennington, Nathan 1 Rheinboldt, Werner C. 1 Sankaran, Gregory Kumar 1 Sukup, Dwight V. 1 Taş, Kenan 1 Thompson, Harold Bevan 1 Tran, Hoainam 1 Wellford, Landon Carter jun. 1 Whiteman, John Robert 1 Zafer, Ağacık 1 Ziekiewicz 1 Zlámal, Miloš A. all top 5 Serials 21 Journal of Difference Equations and Applications 15 Journal of Mathematical Analysis and Applications 10 Rocky Mountain Journal of Mathematics 7 Computers & Mathematics with Applications 7 Advances in Difference Equations 6 Journal of Computational and Applied Mathematics 6 Proceedings of the American Mathematical Society 5 Mathematical and Computer Modelling 4 Applied Mathematics and Computation 4 Canadian Mathematical Bulletin 4 Journal of Differential Equations 4 Applied Mathematics Letters 4 Dynamic Systems and Applications 3 Panamerican Mathematical Journal 3 SIAM Journal on Mathematical Analysis 3 The Canadian Applied Mathematics Quarterly 3 Electronic Journal of Differential Equations (EJDE) 3 Mathematical Inequalities & Applications 2 Turkish Journal of Mathematics 2 Discrete and Continuous Dynamical Systems 2 Communications in Applied Analysis 2 Journal of Inequalities and Applications 2 Electronic Journal of Qualitative Theory of Differential Equations 2 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 2 Nonlinear Dynamics and Systems Theory 1 Applicable Analysis 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Archiv der Mathematik 1 Czechoslovak Mathematical Journal 1 Journal of Approximation Theory 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Nachrichten 1 Mathematica Slovaca 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Pacific Journal of Mathematics 1 Quaestiones Mathematicae 1 Differential and Integral Equations 1 Georgian Mathematical Journal 1 Filomat 1 ETNA. Electronic Transactions on Numerical Analysis 1 Methods and Applications of Analysis 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 Differential Equations and Dynamical Systems 1 Cubo Matemática Educacional 1 Journal of Applied Mathematics and Computing 1 Mediterranean Journal of Mathematics 1 Rendiconti del Seminario Matematico. Universitá e Politecnico di Torino 1 Kluwer Texts in the Mathematical Sciences 1 International Journal of Difference Equations 1 Journal of Mathematical Inequalities 1 Applicable Analysis and Discrete Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Applied Analysis and Computation 1 Universitext all top 5 Fields 117 Difference and functional equations (39-XX) 96 Ordinary differential equations (34-XX) 27 Real functions (26-XX) 5 General and overarching topics; collections (00-XX) 5 Systems theory; control (93-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Numerical analysis (65-XX) 3 Operator theory (47-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 2 Integral transforms, operational calculus (44-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 159 Publications have been cited 6,036 times in 3,004 Documents Cited by ▼ Year ▼ Dynamic equations on time scales. An introduction with applications. Zbl 0978.39001Bohner, Martin; Peterson, Allan 1,450 2001 Advances in dynamic equations on time scales. Zbl 1025.34001 933 2003 Inequalities on time scales: a survey. Zbl 1021.34005Agarwal, R.; Bohner, M.; Peterson, A. 323 2001 Dynamic equations on time scales: A survey. Zbl 1020.39008Agarwal, Ravi; Bohner, Martin; O’Regan, Donal; Peterson, Allan 269 2002 Discrete fractional calculus. Zbl 1350.39001Goodrich, Christopher; Peterson, Allan C. 220 2015 Difference equations: an introduction with applications. Zbl 0733.39001Kelley, Walter G.; Peterson, Allan C. 181 1991 Three positive fixed points of nonlinear operators on ordered Banach spaces. Zbl 1005.47051Avery, R. I.; Peterson, A. C. 169 2001 Difference equations. An introduction with applications. 2nd ed. Zbl 0970.39001Kelley, Walter G.; Peterson, Allan C. 165 2001 Discrete Hamiltonian systems. Difference equations, continued fractions, and Riccati equations. Zbl 0860.39001Ahlbrandt, Calvin D.; Peterson, Allan C. 160 1996 Positive solutions for a nonlinear differential equation on a measure chain. Zbl 0963.34020Erbe, L.; Peterson, A. 105 2000 First and second order linear dynamic equations on time scales. Zbl 0993.39010Bohner, Martin; Peterson, Allan 97 2001 Oscillation criteria for second-order nonlinear delay dynamic equations. Zbl 1125.34046Erbe, L.; Peterson, A.; Saker, S. H. 79 2007 Oscillation criteria for second-order nonlinear dynamic equations on time scales. Zbl 1050.34042Erbe, Lynn; Peterson, Allan; Saker, S. H. 75 2003 Green’s functions and comparison theorems for differential equations on measure chains. Zbl 0938.34027Erbe, Lynn; Peterson, Allan 66 1999 Oscillation for nonlinear second order dynamic equations on a time scale. Zbl 1061.34018Bohner, Martin; Erbe, Lynn; Peterson, Allan 60 2005 Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales. Zbl 1075.39010Erbe, L.; Peterson, A.; Saker, S. H. 49 2005 Hille and Nehari type criteria for third-order dynamic equations. Zbl 1128.39009Erbe, L.; Peterson, A.; Saker, S. H. 46 2007 The theory of differential equations. Classical and qualitative. 2nd ed. Zbl 1201.34001Kelley, Walter G.; Peterson, Allan C. 43 2010 Oscillation criteria for nonlinear damped dynamic equations on time scales. Zbl 1162.39005Erbe, Lynn; Hassan, Taher S.; Peterson, Allan 40 2008 Boundedness and oscillation for nonlinear dynamic equations on a time scale. Zbl 1055.39007Erbe, Lynn; Peterson, Allan 38 2004 Three positive solutions to a discrete focal boundary value problem. Zbl 1001.39021Anderson, D.; Avery, R.; Peterson, A. 38 1998 Comparison theorems for linear dynamic equations on time scales. Zbl 1034.34042Erbe, Lynn; Peterson, Allan; Řehák, Pavel 37 2002 Convexity for nabla and delta fractional differences. Zbl 1320.39003Baoguo, Jia; Erbe, Lynn; Peterson, Allan 37 2015 Two monotonicity results for nabla and delta fractional differences. Zbl 1327.39011Jia, Baoguo; Erbe, Lynn; Peterson, Allan 37 2015 Oscillation criteria for second-order matrix dynamic equations on a time scale. Zbl 1017.34030Erbe, Lynn; Peterson, Allan 36 2002 Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. Zbl 1193.34135Erbe, Lynn; Hassan, Taher S.; Peterson, Allan 35 2009 Oscillation criteria for half-linear delay dynamic equations on time scales. Zbl 1173.34037Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H. 35 2009 Eigenvalue conditions and positive solutions. Zbl 0949.34015Erbe, Lynn; Peterson, Allan 31 2000 Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions. Zbl 1422.39027Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan 29 2016 Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation. Zbl 1145.34329Erbe, L.; Peterson, A.; Saker, S. H. 29 2006 Existence-uniqueness for focal-point boundary value problems. Zbl 0473.34009Peterson, Allan C. 28 1981 Oscillation of third order nonlinear functional dynamic equations on time scales. Zbl 1213.34116Erbe, Lynn; Hassan, Taher S.; Peterson, Allan 28 2010 Boundary value problems for an \(n\)th order linear difference equation. Zbl 0532.39001Peterson, Allan C. 28 1984 Nabla dynamic equations on time scales. Zbl 1032.39007Anderson, Douglas; Bullock, John; Erbe, Lynn; Peterson, Allan; Tran, Hoainam 27 2003 Multiple positive solutions of a discrete second order conjugate problem. Zbl 0959.39006Avery, Richard I.; Peterson, Allan C. 24 1998 Oscillation of second order linear matrix difference equations. Zbl 0762.39005Peterson, Allan 23 1991 Three point boundary value problems on time scales. Zbl 1078.39016Peterson, A. C.; Raffoul, Y. N.; Tisdell, C. C. 23 2004 Henstock-Kurzweil delta and nabla integrals. Zbl 1110.26011Peterson, Allan; Thompson, Bevan 22 2006 Comparison of eigenvalues for focal point problems for \(n\)-th order difference equations. Zbl 0733.39002Hankerson, Darrel; Peterson, Allan 22 1990 A survey of exponential function on times scales. Zbl 1074.39018Bohner, Martin; Peterson, Allan 21 2001 On the existence and uniqueness of solutions to boundary value problems on time scales. Zbl 1089.39005Henderson, Johnny; Peterson, Allan; Tisdell, Christopher C. 21 2004 Weighted Hardy-type inequalities on time scales with applications. Zbl 1342.26064Saker, S. H.; Mahmoud, R. R.; Peterson, A. 21 2016 Exponential stability of dynamic equations on time scales. Zbl 1100.39013Peterson, Allan C.; Raffoul, Youssef N. 21 2005 Monotonicity results for delta fractional differences revisited. Zbl 06760211Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan 20 2017 The \((n,n)\)-disconjugacy of a \(2n\)-th order linear difference equation. Zbl 0815.39003Ahlbrandt, C. D.; Peterson, A. 20 1994 Monotonicity and convexity for nabla fractional \((q,h)\)-differences. Zbl 1364.39009Du, Feifei; Jia, Baoguo; Erbe, Lynn; Peterson, Allan 20 2016 Discrete linear Hamiltonian systems: A survey. Zbl 0942.39009Agarwal, Ravi; Ahlbrandt, Calvin; Bohner, Martin; Peterson, Allan 20 1999 Existence and uniqueness theorems for nonlinear difference equations. Zbl 0625.39002Peterson, Allan C. 20 1987 Kamenev-type oscillation criteria for second-order linear delay dynamic equations. Zbl 1104.34026Erbe, L.; Peterson, A.; Saker, S. H. 19 2006 Boundedness and uniqueness of solutions to dynamic equations on time scales. Zbl 1072.39017Peterson, Allan C.; Tisdell, Christopher C. 18 2004 Riccati equations on a measure chain. Zbl 1008.34006Erbe, Lynn; Peterson, Allan 17 2001 The \((2,2)\)-disconjugacy of the fourth order difference equation. Zbl 0837.39004Peterson, Allan; Ridenhour, Jerry 17 1995 Laplace transform and \(Z\)-transform: Unification and extension. Zbl 1031.44001Bohner, Martin; Peterson, Allan 16 2002 Asymptotic behavior of solutions of a two term difference equation. Zbl 0809.39006Peil, Timothy; Peterson, Allan 16 1994 Existence, multiplicity and nonexistence of positive solutions to a differential equation on a measure chain. Zbl 0937.34025Erbe, Lynn; Peterson, Allan; Mathsen, Ronald 14 2000 Oscillation of solution to second-order half-linear delay dynamic equations on time scales. Zbl 1345.34150Wu, Hongwu; Erbe, Lynn; Peterson, Allan 14 2016 Some relations between the Caputo fractional difference operators and integer-order differences. Zbl 1321.39024Jia, Baoguo; Erbe, Lynn; Peterson, Allan 14 2015 Comparison theorems for eigenvalue problems for \(n\)-th order differential equations. Zbl 0692.34020Hankerson, Darrel; Peterson, Allan 14 1988 Spectral parameter power series for Sturm-Liouville equations on time scales. Zbl 1245.34088Erbe, Lynn; Mert, Raziye; Peterson, Allan 13 2012 Existence-uniqueness for ordinary differential equations. Zbl 0386.34022Peterson, Allan C. 13 1978 Green’s functions for focal type boundary value problems. Zbl 0387.34014Peterson, Allan 13 1979 Bounds for positive solutions for a focal boundary value problem. Zbl 0933.39040Atici, F.; Peterson, A. 13 1998 Comparison theorems and existence theorems for ordinary differential equations. Zbl 0342.34008Peterson, Allan C. 13 1976 Oscillation of third order functional dynamic equations with mixed arguments on time scales. Zbl 1213.34115Erbe, Lynn; Hassan, Taher S.; Peterson, Allan 12 2010 Kiguradze-type oscillation theorems for second order superlinear dynamic equations on time scales. Zbl 1246.34066Baoguo, Jia; Erbe, Lynn; Peterson, Allan 12 2011 On the asymptotic behavior of solutions of Emden-Fowler equations on time scales. Zbl 1259.34093Erbe, Lynn; Baoguo, Jia; Peterson, Allan 12 2012 Monotonicity and convexity for nabla fractional \(q\)-differences. Zbl 1362.39020Baoguo, Jia; Erbe, Lynn; Peterson, Allan 11 2016 Oscillation results for a dynamic equation on a time scale. Zbl 1002.39024Akin, Elvan; Erbe, Lynn; Peterson, Allan; Kaymakçalan, Billur 11 2001 Oscillation of even order nonlinear delay dynamic equations on time scales. Zbl 1274.34262Erbe, Lynn; Mert, Raziye; Peterson, Allan; Zafer, Ağacık 11 2013 Criteria for \(C\)-disfocality of a selfadjoint vector difference equation. Zbl 0802.39003Peil, Timothy; Peterson, Allan 11 1993 Comparison theorems and asymptotic behavior of solutions of discrete fractional equations. Zbl 1349.39006Jia, Baoguo; Erbe, Lynn; Peterson, Allan 11 2015 Hille-Kneser-type criteria for second-order dynamic equations on time scales. Zbl 1229.34136Erbe, Lynn; Peterson, Allan C.; Saker, Samir H. 11 2006 Oscillation of second order superlinear dynamic equations with damping on time scales. Zbl 1189.34133Hassan, Taher S.; Erbe, Lynn; Peterson, Allan 10 2010 Belohorec-type oscillation theorem for second order sublinear dynamic equations on time scales. Zbl 1229.34135Erbe, Lynn; Jia, Baoguo; Peterson, Allan 10 2011 A positivity result applied to difference equations. Zbl 0695.39004Hankerson, Darrel; Peterson, Allan 10 1989 Oscillation of an Euler-Cauchy dynamic equation. Zbl 1052.39007Huff, S.; Olumolode, G.; Pennington, N.; Peterson, A. 10 2003 Existence of solutions to second-order BVPs on time scales. Zbl 1088.39014Erbe, Lynn; Peterson, Allan; Tisdell, Christopher C. 9 2005 On the sign of Green’s functions. Zbl 0292.34013Peterson, Allan C. 9 1976 Oscillation of \(n\)th order superlinear dynamic equations on time scales. Zbl 1216.34100Erbe, Lynn; Baoguo, Jia; Peterson, Allan 9 2011 Delay dynamic equations with stability. Zbl 1134.39011Anderson, Douglas R.; Krueger, Robert J.; Peterson, Allan C. 9 2006 Distribution of zeros of solutions of a fourth order differential equation. Zbl 0183.35901Peterson, A. C. 9 1969 Sturm Liouville equations in the frame of fractional operators with exponential kernels and their discrete versions. Zbl 1429.34007Abdeljawad, Thabet; Mert, Raziye; Peterson, Allan 8 2019 Some Bennett-Copson type inequalities on time scales. Zbl 1339.26067Saker, S. H.; Mahmoud, R. R.; Peterson, A. 8 2016 Green’s functions for (k,n-k)-boundary value problems for linear difference equations. Zbl 0621.39001Peterson, Allan C. 8 1987 Oscillation criteria for a forced second-order nonlinear dynamic equation. Zbl 1168.34025Erbe, L.; Peterson, A.; Saker, S. H. 8 2008 A disconjugacy criterion of W. T. Reid for difference equations. Zbl 0744.34037Peterson, Allan; Ridenhour, Jerry 7 1992 Nonoscillation for second order sublinear dynamic equations on time scales. Zbl 1187.34128Erbe, Lynn; Baoguo, Jia; Peterson, Allan 7 2009 A general reduction of order theorem for discrete linear symplectic systems. Zbl 1304.39002Ahlbrandt, C. D.; Peterson, A. C. 7 1998 A Wong-type oscillation theorem for second order linear dynamic equations on time scales. Zbl 1193.34179Baoguo, Jia; Erbe, Lynn; Peterson, Allan 7 2010 An oscillation theorem for second order superlinear dynamic equations on time scales. Zbl 1297.34100Baoguo, Jia; Erbe, Lynn; Peterson, Allan 7 2013 \(C\)-disfocality for linear Hamiltonian difference systems. Zbl 0818.39003Peterson, Allan 7 1994 Disconjugacy for a third order linear difference equation. Zbl 0809.39005Henderson, J.; Peterson, A. 7 1994 Comparison theorems for a right disfocal eigenvalue problem. Zbl 0882.34079Diaz, Jerry; Peterson, Allan 7 1994 Upper bounds for the distances between consecutive zeros of solutions of first order delay differential equations. Zbl 1320.34099Wu, Hongwu; Erbe, Lynn; Peterson, Allan 7 2015 A unified approach to Copson and Beesack type inequalities on time scales. Zbl 1403.26023Saker, S. H.; Mahmoud, R. R.; Peterson, A. 7 2018 Two asymptotic results of solutions for nabla fractional \((q,h)\)-difference equations. Zbl 1424.39047Du, Feifei; Erbe, Lynn; Jia, Baoguo; Peterson, Allan 7 2018 Oscillation and nonoscillation of solutions of second order linear dynamic equations with integrable coefficients on time scales. Zbl 1191.34109Erbe, Lynn; Jia, Baoguo; Peterson, Allan 7 2009 Focal Green’s functions for fourth-order differential equations. Zbl 0439.34026Peterson, Allan C. 6 1980 Asymptotic properties of solutions to a \(2n\)th-order differential equation on a time scale. Zbl 0963.34042Anderson, D.; Peterson, A. 6 2000 Interval oscillation criteria for forced second-order nonlinear delay dynamic equations with oscillatory potential. Zbl 1202.34162Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H. 6 2010 A Sturm-Liouville approach for continuous and discrete Mittag-Leffler kernel fractional operators. Zbl 1491.34018Mert, Raziye; Abdeljawad, Thabet; Peterson, Allan 1 2021 Sturm Liouville equations in the frame of fractional operators with exponential kernels and their discrete versions. Zbl 1429.34007Abdeljawad, Thabet; Mert, Raziye; Peterson, Allan 8 2019 Gronwall’s inequality for a nabla fractional difference system with a retarded argument and an application. Zbl 1429.39004Chen, Churong; Mert, Raziye; Jia, Baoguo; Erbe, Lynn; Peterson, Allan 5 2019 A generalized \(h\)-fractional Gronwall’s inequality and its applications for nonlinear \(h\)-fractional difference systems with ‘maxima’. Zbl 1421.39002Liu, Xiang; Peterson, Allan; Jia, Baoguo; Erbe, Lynn 4 2019 Asymptotic behavior of solutions of fractional nabla \(q\)-difference equations. Zbl 1414.39003Jia, Baoguo; Erbe, Lynn; Peterson, Allan 4 2019 Stability analysis for a class of nabla \((q,h)\)-fractional difference equations. Zbl 1410.39030Liu, Xiang; Jia, Baoguo; Erbe, Lynn; Peterson, Allan 3 2019 A unified approach to Copson and Beesack type inequalities on time scales. Zbl 1403.26023Saker, S. H.; Mahmoud, R. R.; Peterson, A. 7 2018 Two asymptotic results of solutions for nabla fractional \((q,h)\)-difference equations. Zbl 1424.39047Du, Feifei; Erbe, Lynn; Jia, Baoguo; Peterson, Allan 7 2018 Asymptotic behavior of nabla half order \(h\)-difference equations. Zbl 1457.39005Jia, Baoguo; Du, Feifei; Erbe, Lynn; Peterson, Allan 3 2018 Monotonicity results for delta fractional differences revisited. Zbl 06760211Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan 20 2017 The relation between nabla fractional differences and nabla integer differences. Zbl 1488.26011Baoguo, Jia; Erbe, Lynn; Goodrich, Christopher; Peterson, Allan 5 2017 Liapunov functional and stability of linear nabla \((q,h)\)-fractional difference equations. Zbl 1406.39021Jia, Baoguo; Chen, Siyuan; Erbe, Lynn; Peterson, Allan 4 2017 Existence and rapid convergence results for nonlinear Caputo nabla fractional difference equations. Zbl 1413.39009Liu, Xiang; Jia, Baoguo; Erbe, Lynn; Peterson, Allan 3 2017 Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions. Zbl 1422.39027Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan 29 2016 Weighted Hardy-type inequalities on time scales with applications. Zbl 1342.26064Saker, S. H.; Mahmoud, R. R.; Peterson, A. 21 2016 Monotonicity and convexity for nabla fractional \((q,h)\)-differences. Zbl 1364.39009Du, Feifei; Jia, Baoguo; Erbe, Lynn; Peterson, Allan 20 2016 Oscillation of solution to second-order half-linear delay dynamic equations on time scales. Zbl 1345.34150Wu, Hongwu; Erbe, Lynn; Peterson, Allan 14 2016 Monotonicity and convexity for nabla fractional \(q\)-differences. Zbl 1362.39020Baoguo, Jia; Erbe, Lynn; Peterson, Allan 11 2016 Some Bennett-Copson type inequalities on time scales. Zbl 1339.26067Saker, S. H.; Mahmoud, R. R.; Peterson, A. 8 2016 Oscillation criteria for second order sublinear dynamic equations with oscillating coefficients. Zbl 1347.34140Wu, Hongwu; Jia, Baoguo; Erbe, Lynn; Peterson, Allan 2 2016 Discrete fractional calculus. Zbl 1350.39001Goodrich, Christopher; Peterson, Allan C. 220 2015 Convexity for nabla and delta fractional differences. Zbl 1320.39003Baoguo, Jia; Erbe, Lynn; Peterson, Allan 37 2015 Two monotonicity results for nabla and delta fractional differences. Zbl 1327.39011Jia, Baoguo; Erbe, Lynn; Peterson, Allan 37 2015 Some relations between the Caputo fractional difference operators and integer-order differences. Zbl 1321.39024Jia, Baoguo; Erbe, Lynn; Peterson, Allan 14 2015 Comparison theorems and asymptotic behavior of solutions of discrete fractional equations. Zbl 1349.39006Jia, Baoguo; Erbe, Lynn; Peterson, Allan 11 2015 Upper bounds for the distances between consecutive zeros of solutions of first order delay differential equations. Zbl 1320.34099Wu, Hongwu; Erbe, Lynn; Peterson, Allan 7 2015 A new Picone’s dynamic inequality on time scales with applications. Zbl 1323.26029Saker, S. H.; Mahmoud, R. R.; Peterson, A. 2 2015 Nabla discrete fractional Grüss type inequality. Zbl 1372.39010Güvenilir, A. Feza; Kaymakçalan, Billur; Peterson, Allan C.; Taş, Kenan 3 2014 A Butler-type oscillation theorem for second-order dynamic equations on discrete timescales. Zbl 1304.34160Jia, Baoguo; Erbe, Lynn; Peterson, Allan 1 2014 Oscillation of even order nonlinear delay dynamic equations on time scales. Zbl 1274.34262Erbe, Lynn; Mert, Raziye; Peterson, Allan; Zafer, Ağacık 11 2013 An oscillation theorem for second order superlinear dynamic equations on time scales. Zbl 1297.34100Baoguo, Jia; Erbe, Lynn; Peterson, Allan 7 2013 Spectral parameter power series for Sturm-Liouville equations on time scales. Zbl 1245.34088Erbe, Lynn; Mert, Raziye; Peterson, Allan 13 2012 On the asymptotic behavior of solutions of Emden-Fowler equations on time scales. Zbl 1259.34093Erbe, Lynn; Baoguo, Jia; Peterson, Allan 12 2012 Oscillation theorems for second order sublinear dynamic equations on time scales. Zbl 1269.34073Jia, Baoguo; Erbe, Lynn; Peterson, Allan 4 2012 Asymptotic behavior of \(n\)-th order dynamic equations. Zbl 1279.34106Erbe, L.; Hovhannisyan, G.; Peterson, A. 2 2012 Kiguradze-type oscillation theorems for second order superlinear dynamic equations on time scales. Zbl 1246.34066Baoguo, Jia; Erbe, Lynn; Peterson, Allan 12 2011 Belohorec-type oscillation theorem for second order sublinear dynamic equations on time scales. Zbl 1229.34135Erbe, Lynn; Jia, Baoguo; Peterson, Allan 10 2011 Oscillation of \(n\)th order superlinear dynamic equations on time scales. Zbl 1216.34100Erbe, Lynn; Baoguo, Jia; Peterson, Allan 9 2011 Oscillation criteria for second order sublinear dynamic equations with damping term. Zbl 1228.34146Hassan, Taher S.; Erbe, Lynn; Peterson, Allan 4 2011 Asymptotic behavior of \(n\)-th order sublinear dynamic equations on time scales. Zbl 1235.34239Baoguo, Jia; Erbe, Lynn; Peterson, Allan 2 2011 The theory of differential equations. Classical and qualitative. 2nd ed. Zbl 1201.34001Kelley, Walter G.; Peterson, Allan C. 43 2010 Oscillation of third order nonlinear functional dynamic equations on time scales. Zbl 1213.34116Erbe, Lynn; Hassan, Taher S.; Peterson, Allan 28 2010 Oscillation of third order functional dynamic equations with mixed arguments on time scales. Zbl 1213.34115Erbe, Lynn; Hassan, Taher S.; Peterson, Allan 12 2010 Oscillation of second order superlinear dynamic equations with damping on time scales. Zbl 1189.34133Hassan, Taher S.; Erbe, Lynn; Peterson, Allan 10 2010 A Wong-type oscillation theorem for second order linear dynamic equations on time scales. Zbl 1193.34179Baoguo, Jia; Erbe, Lynn; Peterson, Allan 7 2010 Interval oscillation criteria for forced second-order nonlinear delay dynamic equations with oscillatory potential. Zbl 1202.34162Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H. 6 2010 Oscillation of sublinear Emden-Fowler dynamic equations on time scales. Zbl 1191.34107Baoguo, Jia; Erbe, Lynn; Peterson, Allan 5 2010 Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. Zbl 1193.34135Erbe, Lynn; Hassan, Taher S.; Peterson, Allan 35 2009 Oscillation criteria for half-linear delay dynamic equations on time scales. Zbl 1173.34037Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H. 35 2009 Nonoscillation for second order sublinear dynamic equations on time scales. Zbl 1187.34128Erbe, Lynn; Baoguo, Jia; Peterson, Allan 7 2009 Oscillation and nonoscillation of solutions of second order linear dynamic equations with integrable coefficients on time scales. Zbl 1191.34109Erbe, Lynn; Jia, Baoguo; Peterson, Allan 7 2009 Oscillation of a family of \(q\)-difference equations. Zbl 1170.39002Baoguo, Jia; Erbe, Lynn; Peterson, Allan 5 2009 Oscillation criteria for first order forced dynamic equations. Zbl 1299.34293Erbe, Lynn; Hassan, Taher S.; Peterson, Allan 1 2009 Oscillation criteria for nonlinear damped dynamic equations on time scales. Zbl 1162.39005Erbe, Lynn; Hassan, Taher S.; Peterson, Allan 40 2008 Oscillation criteria for a forced second-order nonlinear dynamic equation. Zbl 1168.34025Erbe, L.; Peterson, A.; Saker, S. H. 8 2008 Basic existence, uniqueness and approximation results for positive solutions to nonlinear dynamic equations on time scales. Zbl 1158.34025Erbe, L.; Peterson, A.; Tisdell, Christopher C. 6 2008 New comparison and oscillation theorems for second-order half-linear dynamic equations on time scales. Zbl 1165.34340Jia, Baoguo; Erbe, Lynn; Peterson, Allan 4 2008 Oscillation criteria for second-order nonlinear delay dynamic equations. Zbl 1125.34046Erbe, L.; Peterson, A.; Saker, S. H. 79 2007 Hille and Nehari type criteria for third-order dynamic equations. Zbl 1128.39009Erbe, L.; Peterson, A.; Saker, S. H. 46 2007 Recent results concerning dynamic equations on time scales. Zbl 1177.34008Erbe, Lynn; Peterson, Allan 4 2007 Some new comparison results for second order linear dynamic equations. Zbl 1201.34142Baoguo, Jia; Erbe, Lynn; Peterson, Allan 2 2007 Integral comparison theorems for second-order linear dynamic equations. Zbl 1127.39029Erbe, Lynn; Peterson, Allan; Řehák, Pavel 2 2007 Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation. Zbl 1145.34329Erbe, L.; Peterson, A.; Saker, S. H. 29 2006 Henstock-Kurzweil delta and nabla integrals. Zbl 1110.26011Peterson, Allan; Thompson, Bevan 22 2006 Kamenev-type oscillation criteria for second-order linear delay dynamic equations. Zbl 1104.34026Erbe, L.; Peterson, A.; Saker, S. H. 19 2006 Hille-Kneser-type criteria for second-order dynamic equations on time scales. Zbl 1229.34136Erbe, Lynn; Peterson, Allan C.; Saker, Samir H. 11 2006 Delay dynamic equations with stability. Zbl 1134.39011Anderson, Douglas R.; Krueger, Robert J.; Peterson, Allan C. 9 2006 Monotone solutions of dynamic systems on time scales. Zbl 1098.39010Erbe, L.; Peterson, A.; Tisdell, C. C. 2 2006 Oscillation for nonlinear second order dynamic equations on a time scale. Zbl 1061.34018Bohner, Martin; Erbe, Lynn; Peterson, Allan 60 2005 Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales. Zbl 1075.39010Erbe, L.; Peterson, A.; Saker, S. H. 49 2005 Exponential stability of dynamic equations on time scales. Zbl 1100.39013Peterson, Allan C.; Raffoul, Youssef N. 21 2005 Existence of solutions to second-order BVPs on time scales. Zbl 1088.39014Erbe, Lynn; Peterson, Allan; Tisdell, Christopher C. 9 2005 Square integrability of Gaussian bells on time scales. Zbl 1088.81058Erbe, L.; Peterson, A.; Simon, M. 3 2005 Comparison theorems of Hille-Wintner type for dynamic equations on time scales. Zbl 1078.39015Erbe, Lynn; Peterson, Allan 1 2005 Boundedness and oscillation for nonlinear dynamic equations on a time scale. Zbl 1055.39007Erbe, Lynn; Peterson, Allan 38 2004 Three point boundary value problems on time scales. Zbl 1078.39016Peterson, A. C.; Raffoul, Y. N.; Tisdell, C. C. 23 2004 On the existence and uniqueness of solutions to boundary value problems on time scales. Zbl 1089.39005Henderson, Johnny; Peterson, Allan; Tisdell, Christopher C. 21 2004 Boundedness and uniqueness of solutions to dynamic equations on time scales. Zbl 1072.39017Peterson, Allan C.; Tisdell, Christopher C. 18 2004 Cauchy functions and Taylor’s formula for time scales \(\mathbb T\). Zbl 1065.39032Higgins, Raegan J.; Peterson, Allan 6 2004 Some recent results in linear and nonlinear oscillation. Zbl 1073.34033Erbe, Lynn; Peterson, Allan 1 2004 Advances in dynamic equations on time scales. Zbl 1025.34001 933 2003 Oscillation criteria for second-order nonlinear dynamic equations on time scales. Zbl 1050.34042Erbe, Lynn; Peterson, Allan; Saker, S. H. 75 2003 Nabla dynamic equations on time scales. Zbl 1032.39007Anderson, Douglas; Bullock, John; Erbe, Lynn; Peterson, Allan; Tran, Hoainam 27 2003 Oscillation of an Euler-Cauchy dynamic equation. Zbl 1052.39007Huff, S.; Olumolode, G.; Pennington, N.; Peterson, A. 10 2003 An oscillation result for a nonlinear dynamic equation on a time scale. Zbl 1086.39004Erbe, Lynn; Peterson, Allan 5 2003 Dynamic equations on time scales: A survey. Zbl 1020.39008Agarwal, Ravi; Bohner, Martin; O’Regan, Donal; Peterson, Allan 269 2002 Comparison theorems for linear dynamic equations on time scales. Zbl 1034.34042Erbe, Lynn; Peterson, Allan; Řehák, Pavel 37 2002 Oscillation criteria for second-order matrix dynamic equations on a time scale. Zbl 1017.34030Erbe, Lynn; Peterson, Allan 36 2002 Laplace transform and \(Z\)-transform: Unification and extension. Zbl 1031.44001Bohner, Martin; Peterson, Allan 16 2002 Averaging techniques for self-adjoint matrix equations on a measure chain. Zbl 1014.39005Erbe, Lynn; Peterson, Allan 3 2002 Existence of bounded solutions for second order dynamic equations. Zbl 1005.39018Akin, Elvan; Bohner, Martin; Erbe, Lynn; Peterson, Allan 2 2002 Prediction of swerving motion of a dual-spin projectile with lateral pulse jets in atmospheric flight. Zbl 1054.70021Burchett, B.; Peterson, A.; Costello, M. 1 2002 Dynamic equations on time scales. An introduction with applications. Zbl 0978.39001Bohner, Martin; Peterson, Allan 1,450 2001 Inequalities on time scales: a survey. Zbl 1021.34005Agarwal, R.; Bohner, M.; Peterson, A. 323 2001 Three positive fixed points of nonlinear operators on ordered Banach spaces. Zbl 1005.47051Avery, R. I.; Peterson, A. C. 169 2001 Difference equations. An introduction with applications. 2nd ed. Zbl 0970.39001Kelley, Walter G.; Peterson, Allan C. 165 2001 First and second order linear dynamic equations on time scales. Zbl 0993.39010Bohner, Martin; Peterson, Allan 97 2001 A survey of exponential function on times scales. Zbl 1074.39018Bohner, Martin; Peterson, Allan 21 2001 Riccati equations on a measure chain. Zbl 1008.34006Erbe, Lynn; Peterson, Allan 17 2001 Oscillation results for a dynamic equation on a time scale. Zbl 1002.39024Akin, Elvan; Erbe, Lynn; Peterson, Allan; Kaymakçalan, Billur 11 2001 ...and 59 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,229 Authors 116 Agarwal, Ravi P. 107 Bohner, Martin J. 80 Peterson, Allan C. 62 Henderson, Johnny Lee 61 Erbe, Lynn Harry 60 O’Regan, Donal 58 Saker, Samir H. 55 Anderson, Douglas Robert 43 Li, Tongxing 43 Šimon Hilscher, Roman 41 Li, Yongkun 41 Torres, Delfim Fernando Marado 39 Abdeljawad, Thabet 39 Ge, Weigao 38 Goodrich, Christopher S. 35 Wong, Patricia J. 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