Dual sets of envelopes and characteristic regions of quasi-polynomials

Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomials

Volumn , Issue , 2009, Pages 1-227

  Cheng, Sui Sun ^a   Lin, Yi Zhong ^b  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

^b FUJIAN NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84967638099     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/7338     Document Type: Book

References (40)

1. S. J. Bilchev, M. K. Grammatikopoulos and I. P. Stavroulakis, Oscillation criteria in higher-order neutral equation, J. Math. Anal. Appl. 183(1994), 1-24.
2. V. G. Boltyanskii, Envelopes, Popular Lectures in Mathematics, Vol. 12, Macmillian, New York, 1964.
3. L. M. Chen, Necessary and sufficient conditions for oscillation of a class of advanced difference equations, Journal of Fujian Teachers University, Natural Science Edition, 15(4)(1999), 16-21 (in Chinese).
4. L. M. Chen, Y. Z. Lin, Necessary and sufficient conditions for oscillations of a class of functional-differential equations of advanced type, J. Fujian Teachers University, Natural Science Edition, 14(1)(1998), 19-24 (in Chinese).
5. L. M. Chen, Y. Z. Lin and S. S. Cheng, Exact regions of oscillation for a difference equation with six parameters, J. Math. Anal. Appl., 222(1998), 92-109.
6. S. S. Cheng and S. S. Chiou, Exact oscillation regions for real quintic polynomials, Unpublished material, 2005.
7. S. S. Cheng and Y. Z. Lin, Complete characterizations of an oscillatory neutral difference equation, J. Math. Anal. Appl., 221(1998), 73-91.
8. S. S. Cheng and Y. Z. Lin, Exact regions of oscillation for a neutral differential equation, Proc. Royal Soc. Edinburgh (A), 130A(2000), 277-286.
9. S. S. Cheng and Y. Z. Lin, Detection of positive roots of a polynomial with five parameters, J. Compu. Appl. Math., 137(2001), 19-48.
10. S. S. Cheng and Y. Z. Lin, The exact region of oscillation for first order neutral differential equation with delays, Quarterly Appl. Math., 64(3)(2006), 433-445.
11. S. S. Cheng, Y. Z. Lin and T. Rassias, Exact regions of oscillation for a neutral difference equation with five parameters, J. Difference Eq. Appl., 6(2000), 513-534.
12. S. S. Cheng and S. Y. Huang, Regions of oscillation for complex quartic polynomials, unpublished material, 2006.
13. L. P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces, Dover, 2004.
14. A. O. Gel’fond, On quasi-polynomials deviating least from zero on the segment [0, 1], Izvestiya Akad. Nauk SSSR. Ser. Mat. 15, (1951). 9-16. (in Russian)
15. N. D. Hayes, Roots of the transcendental equation associated with a certain difference-differential equation, J. London Math. soc., 25(1950), 226-232.
16. Y. Li, Positive solutions of fourth-order boundary value problems with two parameters, J. Math. Anal. Appl., 281 (2003), 477-484.
17. Y. Z. Lin, Distribution of roots of a class of transcendental equations on the complex plane, J. Fujian Teachers University, Natural Science Edition, 2(4)(1986), no. 4, 35-41 (in Chinese).
18. S. Z. Lin, Oscillation in first order neutral differential equations, Ann. Diff. Eq., 19(3)(2003), 334-336.
19. Y. Z. Lin, Necessary and sufficient condition for the oscillation of a class of higher-order neutral equation, Ann. Diff. Eqs., 11(3)(1995), 297-309.
20. Y. Z. Lin, Necessary and sufficient conditions for oscillation for a class of retarded equations, Acta Math. Sci., (Chinese version) 15(2)(1995), no. 2, 137-140. (in Chinese).
21. Y. Z. Lin, Necessary and sufficient conditions for oscillation of a class of functional-differential equations of mixed type, J. Fujian Teachers University, Natural Science Edition, 11(3)(1995), 1-5 (in Chinese).
22. Y. Z. Lin, Necessary and sufficient condition for the oscillation of a class of first-order neutral equation, Acta Math Scientia, 16(1996), 88-93.
23. Y. Z. Lin, Necessary and sufficient conditions for oscillations of differential equations with advanced arguments, J. Fujian Teachers University, Natural Science Edition, 12(4)(1996), 7-13 (in Chinese).
24. Y. Z. Lin and S. S. Cheng, Complete characterizations of a class of oscillatory difference equations, J. Difference Eq. Appl., 2(1996), pp. 301-313.
25. L. Pontryagin, On the zeros of some transcedental functions, IAN USSR, Math. Series, vol. 6(1942), 115-134.
26. H. S. Ren, On the Accurate Distribution of Characteristic Roots and Stability of Linear Delay Differential Systems, Northeastern Forestry University Press, Harbin, 1999 (in Chinese).
27. H. S. Ren, Exact solutions of a functional differential equation, Appl. Math. E-Notes, 2001(1), 40-46.
28. D. D. Siljak, Nonlinear Systems, John Wiley & Sons, 1969.
29. D. D. Siljak, New algebraic criteria for positive realness, J. Franklin Institute, 291(1971), 19-120.
30. D. D. Siljak and M. D. Siljak, Nonnegativity of Uncertain Polynomials, Mathematical Problems in Engineering, 4(1998), 135-163.
31. R. P. Stanley, Enumerative Combinatorics, Volume 1. Cambridge University Press, 1997.
32. A. W. Roberts and D. E. Varberg, Convex Functions, Academic Press, 1973.
33. E. J. Routh, Stability of a Given State of Motion, London, 1877.
34. A. Hurwitz, Ü ber die Bedingungen unter welchen eine Gleichung nur Wurzeln mit negativen reellen Teilen besitzt, Math. Ann., 46(1895), 273-284.
35. C. Hermite, Extrait d’une lettre de Mr. Ch. Hermite de Paris ‘a Mr. Borchardt de Berlin, sur le nombre des racines d’une ‘equation alg’ebrique comprises entre des limits donees, J. Reine Angew. Math., 52(1856), 39-51.
36. Z. C. Wang, A necessary and sufficient condition for the oscillation of higher-order neutral equation, Tohoku Math. J., 41(1989), 575-588
37. Z. C. Wang, A necessary and sufficient condition for the oscillation of higher-order neutral equation with several delays, Chinese Ann. Math. Ser. B, 12(3)(1991), 242-254.
38. E. M. Wright, Stability criteria and the real roots of a transcendental equation, J. Soc. Indust. Appl. Math., 9(1961), 136-148.
39. J. Z. Liang and S. Y. Chen, Unconditionally stability for third order delay differential equations, J. Shaanxi Normal Univ. Nat. Sci. Ed., 29(1)(2001), 12-16 (in Chinese).
40. I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations, The Clarendon Press, Oxford University Press, New York, 1991.