Publications of Martin Bohner

Click on "Abstract" to view an HTML version of the abstract of the document.
Click on "Download" to download a PDF version of the document.
Click HERE if you want to receive a printed version by regular mail.

110 Oscillation and boundedness of solutions to first and second order forced dynamic equations with mixed nonlinearities (with R. Agarwal). Australian Journal of Mathematical Analysis and Applications, 5(1): 1-12, Article 2 (2008).
109 Ostrowski inequalities on time scales (with T. Matthews). Journal of Inequalities in Pure and Applied Mathematics, 2008. To appear.
108 On the asymptotic integration of nonlinear dynamic equations (with E. Akin-Bohner, S. Djebali, and T. Moussaoui). Advances in Difference Equations, 2008: 17 pages, Aricle ID 739602 (2008).
107 Trench's perturbation theorem for dynamic equations (with S. Stevic). Discrete Dynamics in Nature and Society, 2007: 11 pages, Article ID 75672 (2007).
106 Sturmian and spectral theory for discrete symplectic systems (with O. Dosly and W. Kratz). Transactions of the American Mathematical Society, 2007. To appear.
105 The Grüss inequality on time scales (with T. Matthews). Communications in Mathematical Analysis, 3(1): 1-8 (2007).
104 On the relationship between the classical linearization and optimal derivative (with T. Benouaz). Advances in Dynamical Systems and Applications, 2(1): 41-57 (2007).
103 Elements of stability theory of A. M. Liapunov for dynamic equations on time scales (in Russian, with A. A. Martynyuk). Prikladnaya Mekhanika, 43(9): 3-27 (2007). Translation in Nonlinear Dynamics and Systems Theory 7(3): 225-257 (2007).
102 Oscillation of damped second order nonlinear delay differential equations of Emden-Fowler type (with S. Saker). Advances in Dynamical Systems and Applications, 1(2): 163-182 (2006).
101 Oscillation of second order half-linear dynamic equations on discrete time scales (with S. Saker). International Journal of Difference Equations, 1(2): 205-218 (2006).
100 The convolution on time scales (with G. Guseinov). Abstract and Applied Analysis, 2007: 24 pages, Article ID 58373 (2007).
99 Euler-type boundary value problems in quantum calculus (with T. Hudson). International Journal of Applied Mathematics & Statistics, 9(J07): 19-23 (2007).
98 Double integral calculus of variations on time scales (with G. Guseinov). Computers and Mathematics with Applications, 54(1): 46-57 (2007).
97 A Philos criterion for second-order dynamic equations (with Howard Warth). Selcuk Journal of Applied Mathematics, 7(1): 25-31 (2006).
96 Oscillation criteria for first and second order forced difference equations with mixed nonlinearities (with R. Agarwal, W.-S. Cheung, and S. R. Grace). Mathematical and Computer Modelling, 45(7-8): 965-973 (2007).
95 Periodic solutions of functional dynamic equations with infinite delay (with Li Bi and M. Fan). Nonlinear Analysis, 68(5): 1226-1245 (2008).
94 Multiple Lebesgue integration on time scales (with G. Guseinov). Advances in Difference Equations, 2006: 12 pages, Article ID 26391 (2006).
93 Periodicity of scalar dynamic equations and applications to population models (with M. Fan and J. Zhang). Journal of Mathematical Analysis and Applications, 330(1): 1-9 (2007).
92 Singular second-order multipoint dynamic boundary value problems with mixed derivatives (with H. Luo). Advances in Difference Equations, 2006: 15 pages, Article ID 54989 (2006).
91 The logarithm on time scales. Journal of Difference Equations and Applications, 11(15): 1305-1306 (2005).
90 Existence of periodic solutions in predator-prey and competition dynamic systems (with M. Fan and J. Zhang). Nonlinear Analysis Series B: Real World Applications, 7: 1193-1204 (2006).
89 Asymptotic behavior of second-order dynamic equations (with S. Stevic), Applied Mathematics and Computation, 188: 1503-1512 (2007).
88 An introduction to complex functions on products of two time scales (with G. Guseinov). Journal of Difference Equations and Applications, 12(3-4): 369-384 (2006).
87 Line integrals and Green's formula on time scales (with G. Guseinov), Journal of Mathematical Analysis and Applications, 326: 1124-1141 (2007).
86 Discrete Oscillation Theory (with R. Agarwal, S. Grace, and D. O'Regan). Hindawi Publishing Corporation, 2005.

Click here!

Download a sample
(Preface, Table of Contents, Chapter 1, Bibliography)!
85 Linear and nonlinear nonlocal boundary value problems for differential-operator equations (with R. Agarwal and V. Shakhmurov). Applicable Analysis, 85(6-7): 701-716 (2006).
84 Kneser's theorem in q-calculus (with M. Ünal). Journal of Physics A: Mathematical and General, 38: 6729-6839 (2005).
83 Oscillation and nonoscillation of forced second order dynamic equations (with C. Tisdell). Pacific Journal of Mathematics, 230(1): 59-71 (2007).
82 Second order dynamic inclusions (with C. Tisdell). Journal of Nonlinear Mathematical Physics, 12(2): 36-45 (2005).
81 (Book Review) Oscillation Theory for Second Order Dynamic Equations. By R. Agarwal, S. Grace, and D. O'Regan. SIAM Review, 46(4): 748-751 (2004).
80 Multiple integration on time scales (with G. Guseinov). Dynamic Systems and Applications, 14(3-4): 579-606 (2005).
79 Spectrum and principal vectors of q-difference equations (with M. Adivar). Indian Journal of Mathematics, 48(1): 17-33 (2006).
78 Spectral analysis of q-difference equations with spectral singularities (with M. Adivar). Mathematical and Computer Modelling, 43(7-8): 695-703 (2006).
77 Asymptotic expansion and analytic time scales (with D. Lutz). ZAMM - Zeitschrift für angewandte Mathematik und Mechanik (Journal of Applied Mathematics and Mechanics), 86(1): 37-45 (2006).
76 Pachpatte inequalities on time scales (with E. Akin-Bohner and F. Akin). Journal of Inequalities in Pure and Applied Mathematics, 6(1): 1-23 (2005).
75 Maximal regular boundary value problems in Banach-valued weighted space (with R. Agarwal and V. Shakhmurov). Boundary Value Problems, 1: 9-42 (2005).
74 Floquet theory and stability of nonlinear integro-differential equations (with R. Agarwal, A. Domoshnitsky, and Y. Goltser). Acta Mathematica Hungarica, 109(4): 305-330 (2005).
73 Oscillation for nonlinear second order dynamic equations on time scales (with L. Erbe and A. Peterson). Journal of Mathematical Analysis and Applications, 301: 491-507 (2005).
72 Some oscillation criteria for first order delay dynamic equations. Far East Journal of Applied Mathematics, 18(3): 289-304 (2005).
71 Oscillation criteria for a certain class of second order Emden-Fowler dynamic equations (with E. Akin-Bohner and S. Saker). Electronic Transactions of Numerical Analysis, 27: 1-12 (2007).
70 Nonoscillation and Oscillation Theory of Functional Differential Equations (with R. Agarwal and W. Li). Marcel Dekker, New York, 2004.

Click here!
69 Oscillation of second order delay dynamic equations (with R. Agarwal and S. Saker). The Canadian Applied Mathematics Quarterly, 13(1): 1-17 (2005).
68 Partial differentiation on time scales (with G. Guseinov). Dynamic Systems and Applications, 13: 351-379 (2004).
67 Half-linear dynamic equations: A survey (with R. Agarwal and P. Rehak). In Nonlinear Analysis and Applications, pages 1-58. Kluwer Academic Publishers, Dordrecht, 2003.
66 Miscellaneous dynamic equations (with E. Akin-Bohner). Methods and Applications of Analysis, 10(1): 11-30 (2003).
65 Diagonalization approach to discrete quadratic functionals (with O. Dosly, R. Hilscher and W. Kratz). Archive of Inequalities and Applications, 1(2): 261-274 (2003).
64 Oscillation criteria for perturbed nonlinear dynamic equations (with S. Saker). Mathematical and Computer Modelling, 40(3-4): 249-260 (2004).
63 Positive semidefiniteness of discrete quadratic functionals (with O. Dosly and W. Kratz). Proceedings of the Edinburgh Mathematical Society, 46: 627-636 (2003).
62 Asymptotic behavior of solutions of dynamic equations (with S. Bodine and D. Lutz). Sovremennye problemy matematiki. Fundamental'nye napravleniya (in Russian). Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., 30-39, Moscow, 2003. Translation in Journal of Mathematical Sciences 124(4): 5110-5118 (2004).
61 Oscillation of second order nonlinear dynamic equations on time scales (with S. Saker). Rocky Mountain Journal of Mathematics, 34(4): 1239-1254 (2004).
60 Improper integrals on time scales (with G. Guseinov). Dynamic Systems and Applications, 12(1-2): 45-66 (2003).
59 Boundary value problems on infinite intervals: A topological approach (with R. Agarwal and D. O'Regan), Chapter 9 in Advances in Dynamic Equations on Time Scales, pages 275-291, 2003.
58 Riemann and Lebesgue integration (with G. Guseinov), Chapter 5 in Advances in Dynamic Equations on Time Scales, pages 117-163, 2003.
57 Some dynamic equations (with E. Akin-Bohner), Chapter 2 in Advances in Dynamic Equations on Time Scales, pages 17-46, 2003.
56 Introduction to the time scales calculus (with G. Guseinov and A. Peterson), Chapter 1 in Advances in Dynamic Equations on Time Scales, pages 1-15, 2003.
55 Advances in Dynamic Equations on Time Scales (with A. Peterson). Birkhäuser, Boston, 2003.

Click here!
54 Oscillation of symplectic dynamic systems (with O. Dosly). The Australian and New Zealand Industrial and Applied Mathematics Journal, 46(1): 17-32 (2004).
53 Formulas of Bendixson and Alekseev for difference equations (with V. Lakshmikantham). Bulletin of the London Mathematical Society, 36(1): 65-71 (2004).
52 Exponential functions and Laplace transforms for alpha derivatives (with E. Akin-Bohner). Conference Proceedings of the Sixth International Conference on Difference Equations and Applications, 231-237 (2004).
51 Variable change for Sturm-Liouville differential expression on time scales (with C. Ahlbrandt and T. Voepel). Journal of Difference Equations and Applications, 9(1): 93-107 (2003).
50 Existence of bounded solutions for second order dynamic equations (with E. Akin, L. Erbe, and A. Peterson). Journal of Difference Equations and Applications, 8(4): 389-401 (2002).
49 Perturbations of dynamic equations (with R. Hering). Journal of Difference Equations and Applications, 8(4): 295-305 (2002).
48 An eigenvalue problem for linear Hamiltonian dynamic systems (with R. Hilscher). Fasciculi Mathematici, (35): 35-49 (2005).
47 An oscillation theorem for discrete eigenvalue problems (with O. Dosly and W. Kratz). Rocky Mountain Journal of Mathematics, 33(4):1233-1260.
46 Inequalities on time scales: A survey (with R. Agarwal and A. Peterson). Mathematical Inequalites and Applications, 4(4):535-557 (2001).
45 Laplace transform and Z-transform: Unification and extension (with A. Peterson). Methods and Applications of Analysis, 9(1): 155-162 (2002). Preprint in Ulmer Seminare 6.
44 First and second order linear dynamic equations on time scales (with A. Peterson). Journal of Difference Equations and Applications, 7: 767-792 (2001).
43 Linear Hamiltonian dynamic systems on time scales: Sturmian property of the principal solution (with O. Dosly and R. Hilscher). Nonlinear Analysis, 47: 849-860 (2001).
42 A survey of exponential functions on time scales (with A. Peterson). Revista Cubo Matematica Educacional, 3(2): 285-301 (2001).
41 Dynamic equations on time scales: A survey (with R. Agarwal, D. O'Regan, and A. Peterson). Journal of Computational and Applied Mathematics, 141(1-2): 1-26 (2002). Preprint in Ulmer Seminare 5.
40 Time scale systems on infinite intervals (with R. Agarwal and D. O'Regan). Nonlinear Analysis, 47: 837-848 (2001) .
39 Time scale boundary value problems on infinite intervals (with R. Agarwal and D. O'Regan). Journal of Computational and Applied Mathematics, 141(1-2): 27-34 (2002).
38 Dynamic Equations on Time Scales: An Introduction with Applications (with A. Peterson). Birkhäuser, Boston, 2001.

Download a sample
(Preface, Table of Contents, Chapter 1, Bibliography)!
37 Opial inequalities on time scales (with B. Kaymakcalan). Annales Polonici Mathematici, 77(1-3): 11-20 (2001).
36 Mimetic methods on measure chains (with J. Castillo). Computers and Mathematics with Applications, 42: 705-710 (2001).
35 Lyapunov inequalities for time scales (with S. Clark and J. Ridenhour). Journal of Inequalities and Applications, 7(1): 61-77 (2002).
34 Calculus of variations on time scales. Dynamic Systems and Applications, 13: 339-349, 2004.
33 Higher order dynamic equations on measure chains: Wronskians, disconjugacy, and interpolating families of functions (with P. Eloe). Journal of Mathematical Analysis and Applications, 246: 639-656 (2000).
32 Hamiltonian systems on time scales (with C. Ahlbrandt and J. Ridenhour). Journal of Mathematical Analysis and Applications, 250: 561-578 (2000).
31 Trigonometric systems in oscillation theory of difference equations (with O. Dosly). In Conference Proceedings of the Third International Conference on Dynamic Systems and Applications, Atlanta, 1999. Dynamic Publishers. Proceedings of Dynamic Systems and Applications, 3: 99-104 (2001).
30 The discrete Prüfer transformation (with O. Dosly). Proceedings of the American Mathematical Society, 129(9):2715-2726 (2001).
29 Discrete linear Hamiltonian systems: A survey (with R. P. Agarwal, C. Ahlbrandt, and A. Peterson). Dynamic Systems and Applications, 8(3-4): 307-333 (1999), special issue on Discrete and Continuous Hamiltonian Systems, edited by R. Agarwal and M. Bohner.
28 Asymptotic behavior of dynamic equations on time scales (with D. Lutz). Journal of Difference Equations and Applications, 7(1): 21-50 (2001).
27 (Book Review) Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations. By C. Ahlbrandt and A. Peterson. Journal of Difference Equations and Applications, 5(3): 313-316 (1999).
26 Trigonometric transformations of symplectic difference systems (with O. Dosly). Journal of Differential Equations, 163: 113-129 (2000).
25 Eigenvalues and eigenfunctions of discrete conjugate boundary value problems (with R. P. Agarwal and P. J. Y. Wong). Computers and Mathematics with Applications, 38(3-4): 159-183 (1999).
24 Discrete Reid roundabout theorems (with O. Dosly and W. Kratz). Dynamic Systems and Applications, 8(3-4): 345-352 (1999), special issue on Discrete and Continuous Hamiltonian Systems, edited by R. Agarwal and M. Bohner.
23 Sturm-Liouville eigenvalue problems on time scales (with R. P. Agarwal and P. J. Y. Wong). Applied Mathematics and Computation, 99: 153-166 (1999). Preprint in Research Report No. 714, Department of Mathematics, National University of Singapore.
22 A Sturmian theorem for recessive solutions of linear Hamiltonian difference systems (with O. Dosly and W. Kratz). Applied Mathematics Letters, 12: 101-106 (1999).
21 Basic calculus on time scales and some of its applications (with R. P. Agarwal). Resultate der Mathematik, 35 (1-2): 3-22 (1999). Preprint in Research Report No. 704, Department of Mathematics, National University of Singapore.
20 Positive solutions and eigenvalues of conjugate boundary value problems (with R. P. Agarwal and P. J. Y. Wong). Proceedings of the Edinburgh Mathematical Society, 42: 349-374 (1999). Preprint in Research Report No. 702, Department of Mathematics, National University of Singapore.
19 Quadratic functionals for second order matrix equations on time scales (with R. P. Agarwal). Nonlinear Analysis, 33: 675-692 (1998). Preprint in Research Report No. 701, Department of Mathematics, National University of Singapore.
18 Positivity of block tridiagonal matrices (with O. Dosly). SIAM Journal of Matrix Analysis, 20(1): 182-195 (1998).
17 Discrete Sturmian theory. Mathematical Inequalitites and Applications, 1(3): 375-383 (1998). Preprint in Ulmer Seminare 1.
16 Inequalities and asymptotics for Riccati matrix difference operators (with O. Dosly and W. Kratz). Journal of Mathematical Analysis and Applications, 221(1): 262-286 (1998).
15 Asymptotic behavior of discretized Sturm-Liouville eigenvalue problems. Journal of Difference Equations and Applications, 3: 289-295 (1998).
14 Symplectic systems and related discrete quadratic functionals. Facta Universitatis (Ser. Math. Inform.), 12: 143-156 (1997).
13 Discrete linear Hamiltonian eigenvalue problems. Computers and Mathematics with Applications, 36(10-12): 179-192 (1998).
12 Disconjugacy and transformations for symplectic systems (with O. Dosly). The Rocky Mountain Journal of Mathematics, 27(3): 707-743 (1997).
11 Riccati matrix difference equations and linear Hamiltonian difference systems. Dynamics of Continuous, Discrete and Impulsive Systems, 2(2): 147-159 (1996).
10 On disconjugacy for Sturm-Liouville difference equations. Journal of Difference Equations and Applications, 2(2): 227-237 (1996).
9 Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions. Journal of Mathematical Analysis and Applications, 199(3): 804-826 (1996).
8 An oscillation theorem for a Sturm-Liouville eigenvalue problem. Mathematische Nachrichten, 182: 67-72 (1996).
7 Brain state in a convex body (with S. Hui). IEEE Transactions on Neural Networks, 6(5): 1053-1060 (1995).
6 Positive definiteness of discrete quadratic functionals. In C. Bandle, editor, International Series of Numerical Mathematics, volume 123, pages 55-60, Basel, 1997. Birkhaeuser. General Inequalities 7, Oberwolfach.
5 Inhomogeneous discrete variational problems. In S. Elaydi, I. Gyoeri, and G. Ladas, editors, Conference Proceedings of the Second International Conference on Difference Equations, pages 89-97, Veszprem, 1995. Gordon and Breach.
4 Controllability and disconjugacy for linear Hamiltonian difference systems. In S. Elaydi, J. Graef, G. Ladas, and A. Peterson, editors, Conference Proceedings of the First International Conference on Difference Equations, pages 65-77, San Antonio, 1994. Gordon and Breach.
3 Zur Positivität diskreter quadratischer Funktionale. PhD Thesis, University Ulm, 1995. English Edition: On Positivity of discrete quadratic functionals.
2 Ein Oszillationssatz fuer Sturm-Liouvillesche Eigenwertprobleme. Master's Thesis, University Ulm, 1993.
1 The brain state in a convex body neural model. Master's Thesis, San Diego State University, 1992.