# Edward A. Grove

Department of Mathematics URI

## Professional Information

• Title: Professor of Mathemathics

• Educational Background: Ph.D, Brown University, 1969

## Contact Information

• Office: 245 Tyler Hall
• Telephone: (401) 874-5299
• E-mail: grove@math.uri.edu

## Research Information

• Basic Theory of Nonlinear Difference Equations of Order Greater than One.

• Global Stability and Periodic Behavior of Solutions.

## Books

1. "An Introduction to Complex Variables" (with G. Ladas), Houghton Mifflin, Boston, 1974.

2. "Periodicities in Nonlinear Difference Equations" (with G. Ladas), CRC Press, 2005.

## Publications

1. SU(n) actions on manifolds with vanishing first and second integral Pontrjagin classes, Springer-Verlag. Lecture Notes in Mathematics, 298(1972) 324-333.

2. N-person games for systems of hyperbolic linear partial differential equations (with J. Papadakis), Differential Games and Control Theory, Marcel Dekker, New York, (1974) 27-35.

3. An Introduction to Complex Variables (with G. Ladas), Houghton Mifflin, Boston, 1974. (Book) See above.

4. SU(n) actions on manifolds with vanishing first and second integral Pontrjagin classes, Transactions of the American Mathematical Society, 19(1974) 331-350.

5. Classification of compact homogeneous spaces with non-zero Euler class and with zero Pontrjagin classes (with W.Y. Hsiang), Bull. Inst. Math. Acad. Sinica, Vol. 8, No. 2/3, Part II (July, 1980) 365-382. (Special issue in memory of H.C. Wang.)

6. Oscillations of first order neutral delay differential equations (with M.K. Grammatikopoulos and G. Ladas), J. Math. Anal. Appl., 120(1986) 510-520.

7. Oscillations and asymptotic behavior of neutral differential equations with deviating arguments (with M.K. Grammatikopoulos and G. Ladas), Applicable Anal., 22(1986) 1-19.

8. Sturm comparison theorems for neutral differential equations (with M.R.S. Kulenovic and G. Ladas), Canadian Mathematical Society Conference Proceedings, 8(1987), 163-169.

9. Oscillation and asymptotic behavior of second order neutral differential equations with deviating arguments (with M.K. Grammatikopoulos and G. Ladas), Canadian Mathematical Society Conference Proceedings, 8(1987) 153-161.

10. Sufficient conditions for oscillation and non-oscillation of neutral equations (with M.R.S. Kulenovic and G. Ladas), J. Diff. Eqns., 68(1987), 373-382.

11. A necessary and sufficient condition for the oscillation of neutral equations (with G. Ladas and A. Meimaridou), J. Math. Anal. Appl., 126(1987) 341-354.

12. Oscillations and asymptotic behavior of first-order neutral delay differential equations (with G. Ladas and S.W. Schultz), Applicable Analysis, 27(1988), 67-78.

13. Neutral delay differential equations with positive and negative coefficients (with K. Farrell and G. Ladas), Applicable Analysis, 27(1988), 181-197.

14. Sufficient conditions for the oscillation of delay and neutral delay equations (with G. Ladas and J. Schinas), Canad. Math. Bull., 31(1988), 459-466.

15. Neutral delay differential equations with variable delays (with K. Gopalsamy and G. Ladas), Proceedings of The International Conference on Theory and Applications of Differential Equations, March 21-25, 1988, Ohio University; Differential Equations and Applications, Ohio University Press, 1988, 343-347.

16. On the characteristic equation for equations with continuous and piecewise constant arguments (with I. Gyori and G. Ladas), Radovi Matematicki 5(1989), 271-281.

17. Oscillations of neutral difference equations (with D.A. Georgiou and G. Ladas), Applicable Analysis, 33(1989), 243-253.

18. A Myskis-type comparison result for neutral equations (with M.R.S. Kulenovic and G. Ladas), Mathematische Nachricten, 146(1990), 195-206.

19. Oscillation of neutral difference equations with variable coefficients (with D.A. Georgiou and G. Ladas), Differential Equations: Stability and Control'', Marcel Dekker, 1990, 165-173.

20. A simple model for price fluctuations in a single commodity market (with A.M. Farahani), Oscillation and Dynamics in Delay Equations, American Mathematical Society, 1992, 97-103.

21. Global attractivity in a Food-Limited'' population model (with G. Ladas and Q. Qian), Dynamic Systems and Applications, 2(1993), 243-250.

22. Periodicity in a simple genotype selection model (with V.Lj. Kocic, G. Ladas and R. Levins), Differential Equations and Dynamical Systems, 1(1993) 35-50.

23. Oscillation and stability in a simple genotype model (with V.Lj. Kocic, G. Ladas and R. Levins), Quarterly of Applied Mathematics, 52(1994) 499-508.

24. Oscillation of a difference equation with periodic coefficients (with E. Camouzis and G. Ladas), Applicable Analysis, 53(1994), 143-148.

25. Oscillation and stability in models of a perennial grass (with R. DeVault, G. Ladas, R. Levins and C. Puccia), The Proceedings of Dynamic Systems and Applications - 1, 87-93, Dynamic Publishers Inc., U.S.A., 1994.

26. On a rational recursive sequence (with E.J. Janowski, C.M. Kent and G. Ladas), Communications on Applied Nonlinear Analysis, 1(1994), 61-72.

27. Monotone unstable solutions of difference equations and conditions for boundedness (with E. Camouzis, G. Ladas and V.Lj. Kocic), Journal of Difference Equations and Applications, 1(1995), 17-44.

28. Bounds on the lengths of semi-cycles of difference equations (with R. DeVault, G. Ladas. R. Levins and C. Puccia), Proceedings of the First International Conference on Difference Equations, May 25-28, 1994, San Antonio, Texas, USA, Gordon and Breach Science Publishers (1995), 143-161.

29. Oscillation and stability in a delay model of a perennial grass (with R. DeVault, G. Ladas, R. Levins and C. Puccia), Journal of Difference Equations and Applications, 1(1995), 173-185.

30. Oscillation and stability in a genotype selection model with several delays (with V.Lj. Kocic, G. Ladas and R. Levins), Journal of Difference Equations and Applications, 2(1996), 205-217.

31. Lyness equations with variable coefficients (with C.M. Kent and G. Ladas), Proceedings of the Second International Conference on Difference Equations and Applications, August 7-11, 1995, Vesprem, Hungary, Gordon and Breach Science Publishers, 1997, 281-288.

32. Classification of invariants for certain difference equations (with V.Lj. Kocic and G. Ladas), Proceedings of the Second International Conference on Difference Equations and Applications, August 7-11, 1995, Vesprem, Hungary, Gordon and Breach Science Publishers, 1997, 289-294.

33. On a nonlinear equation with piecewise constant argument (with G. Ladas and S. Zhang), Commun. Appl. Nonlinear Anal., 4(1997), 67-79.

34. Boundedness and persistence of the non-autonomous Lyness and Max equations, (with G. Ladas and C.M. Kent), Journal of Difference Equations and Applications, 3(1998), 241-258.

35. On some difference equations with eventually periodic solutions (with A.M. Amleh, G. Ladas, and C.M. Kent), Journal of Math. Anal. and Applications, 223(1998), 196-215.

36. On the non-autonomous equation x_{n+1} = max { A_{n}/x_{n},B_{n}/x_{n-1}}, (with W.J. Briden, G. Ladas, and L.C. McGrath), Proceedings of the Third International Conference on Difference Equations and Applications, September 1-5, 1997, Taipei, Taiwan, Gordon and Breach Science Publishers, (1999), 49-73.

37. Eventually periodic solutions of x_{n+1} = max { 1/x_{n} , A_{n} /x_{n-1}} (with W.J. Briden, C.M. Kent, and G. Ladas), Commun. Appl. Nonlinear Anal., 6(1999), 31-34.

38. On the recursive sequence x_{n+1} = alpha + x_{n-1}/x_{n} (with A.M. Amleh, D.A. Georgiou, and G. Ladas), Journal of Math. Anal. and Applications, 233(1999), 790-798.

39. On the global behavior of solutions of a biological model (with G. Ladas, R. Levins, and N. Prokup), Commun. Appl. Nonlinear Anal., 7(2000), 33-46.

40. A global convergence result with applications to periodic solutions (with H. El-Metwally and G. Ladas), Journal of Math. Anal. and Applications, 245(2000), 161-170.

41. Global Stability in Some Population Models (with C.M. Kent, G. Ladas, R. Levins and S. Valicenti), Proceedings of the Fourth International Conference on Difference Equations and Applications}, August 27-31, 1998, Poznan, Poland, Gordon and Breach Science Publishers, (2000), 149-176.

42. Existence and Behavior of Solutions of a Rational System (with G. Ladas, L.C. McGrath and C.T. Teixeira), Commun. Appl. Nonlinear Anal., 8(2001), 1-25.

43. On the Global Attractivity and Periodic Character of Some Difference Equations (with H. El-Metwalli, G. Ladas and H. Voulov), Journal of Difference Equations and Applications, 7(2001), 837-850.

44. On the Difference Equation x_{n+1} = max { \frac{1}{x_{n}},\frac{A_{n} }{ x_{n-1}} } with a Period 3 Parameter (with C.M. Kent, G. Ladas and M.A. Radin), Fields Institute Communications Series, Volume 29, 2001.

45. On the difference equation x_{n+1} = a + b x_{n-1}e^{-x_{n}} (with H. El-Metwalli, G. Ladas, R. Levins, and M. Radin), Nonlinear Analysis, 47(2001) 4623-4634.

46. On the global character of y_{n+1} = \frac{ py_{n-1} + y_{n-2} }{ q + y_{n-2} } (with G. Ladas, M. Predescu, and M. Radin), MATH. SCI. RES. HOT-LINE 5(2001), 25-39.

47. Periodicity in Nonlinear Difference Equations (with G. Ladas), Revista Cubo., 4(2002), 195-230.

48. On the Periodic Character of the Difference Equation x_{n+1} = \frac{ p + x_{n-2k} }{ 1 + x_{n-2l} } (with G. Ladas and M. Predescu), Math. Sci. Res. Journal, 6(2002), 221-233.

49. On the Global Character of the Difference Equation x_{n+1} = \frac{ alpha + gamma x_{n-(2k+1)} + \delta x_{n-2l} }{ A + x_{n-2l} } (with G. Ladas, M. Predescu, and M. Radin), Journal of Difference Equations and Applications 9(2003), 171-199.

50. On the Dynamics of y_{n+1} = \frac{ p + y_{n-2} }{ qy_{n-1} + y_{n-2} } (with G. Ladas and L.C. McGrath), Proceedings of the 6th ICDEA, Augsburg, Germany, Taylor and Francis, London, 2003.

51. On the Trichotomy Character of x_{n+1} = \frac{ \alpha + \gamma x_{n-1} }{ A + B x_{n} + x_{n-2} } (with E. Chatterjee, G. Ladas, and Y. Kostrov), Journal of Difference Equations and Applications 9(2003), 1113-1128.

52. On the Difference Equation y_{n+1} = \frac{ y_{n-(2k+1)} + p }{ y_{n-(2k+1)} + qy_{n-2l} } (with H.A. El- Metwally, G. Ladas and L.C. McGrath), New Progress in Difference Equations , CRC, 2004, p.433-453.

53. On Period-two solutions of x_{n+1} = \frac{ \alpha + \beta x_{n} + \gamma x_{n-1} }{ A + B x_{n} + C x_{n-1} } (with G. Ladas), Proceedings of the 7th ICDEA, Taylor and Francis (2004).

54. Progress Report on Rational Difference Equations (with M.R.S Kulenovic and G. Ladas), Journal of Difference Equations (2004).

55. Periodicities in Nonlinear Difference Equations (with G. Ladas), CRC Press, 2005. (Book.) See above.

56. On Third-Order Rational Difference Equations, Part 4 (with Y. Kostrov, G. Ladas, and M. Predescu), Journal of Difference Equations and Applications (2005).

57. Riccati Difference Equations With Real Period-2 Coefficients (with Y. Kostrov, G. Ladas, and S.W. Schultz), Communications on Applied Nonlinear Analysis Volume 14(2007), Number 2, p.33-56

## Personal Interests and Hobbies

• Walking
• Card Games
• My puppy dog Phoenix