Advanced Topics in Difference Equations

by Ravi P. Agarwal

Preface. 1. Periodic Solutions of First Order Linear Equations. 2. Periodic Solutions of Generalized Difference Systems. 3. Periodic Boundary Value First Order Systems. 4. Periodic Boundary Value Second Order Systems. 5. Periodic Solutions of Higher Order Partial Difference Equations. 6. Nonlinear Variation of Parameter One Independent Variable. 7. Nonlinear Variation of Parameter Several Independent Variables. 8. Convergence to Equilibria. 9. Asymptotic Behavior of Generalized Difference Systems. 10. Stability of Generalized Difference Systems. 11. Oscillation via Lyapunov's Second Method. 12. Oscillation via Difference Inequalities. 13. Oscillation via Summation Averages. 14. Oscillation for Nonlinear Difference Equations. 15. Oscillation for Quasilinear Difference Equations. 16. Oscillations Generated by Deviating Arguments. 17. Positive Monotone Solutions for Nonlinear Difference Equations. 18. Oscillation for nth Order Nonlinear Difference Equations. 19. Comparison Theorems. 20. Oscillation for Second Order Neutral Delay Difference Equations. 21. Oscillation for Second Order Neutral Delay Difference Equations (Contd.). 22. Oscillation for Higher Order Neutral Delay Difference Equations. 23. Oscillation for Partial Difference Equations I. 24. Oscillation for Partial Difference Equations II. 25. Oscillation for Partial Difference Equations III. 26. Oscillation for Partial Difference Equations IV. 27. A Three-Point Boundary Value Problem. 28. A Singular Boundary Value Problem. 29. Eigenvalues of Boundary Value Problems. 30. Two Solutions of a Boundary Value Problem. 31. (n,p) Boundary Value Problems. 32. Boundary Value Problems Arising in Transport Phenomena. 33. Solutions of m-Point Boundary Value Problems. 34. Two-Point Boundary Value Problems for Generalized Difference Systems. 35. Multi-Point Boundary Value Problems for Generalized Difference Systems. 36. Resonant Boundary Value Problems for Generalized Difference Systems. 37. Boundary Value Problems in Abstract Spaces. 38. Linear Square Optimal Control Problem. 39. Symmetries of Difference Systems on Manifolds. 40. Discrete Polar Coordinates. References.

524 pages, Paperback

First published April 30, 1997