Classifications and existence criteria for positive solutions of systems of nonlinear differential equations

Journal of Mathematical Analysis and Applications

Volumn 298, Issue 2, 2004, Pages 446-462

  Li, Wan Tong ^a   Yang, Xiaojing ^b  

^a LANZHOU UNIVERSITY   (China)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

Classification scheme; Existence; Fixed point theorems; Nonlinear differential systems; Positive solutions

Indexed keywords

EID: 10144232768     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.05.022     Document Type: Article

References (28)

1. Agarwal R.P. Bohner M. Li W.T. Nonoscillation and Oscillation Theory for Functional Differential Equations Pure Appl. Math. 2004 Dekker New York
2. Bainov D.D. Markova N.T. Simeonov P.S. Asymptotic behavior of the nonoscillatory solutions of differential equations of second order with delay depending on the unknown function J. Comput. Appl. Math. 91 1998 87-96
3. Fan X.L. Li W.T. Zhong C.K. A classification scheme for positive solutions of second order nonlinear iterative differential equations Electron. J. Differential Equations 2000 2000 1-14
4. Huo H.F. Li W.T. Oscillation criteria for certain two-dimensional differential systems Internat. J. Appl. Math. 6 2001 253-261
5. Kamenskii G.A. On the asymptotic behavior of solutions of linear differential equations of second order with retarded arguments Notices of the Scientist of MGU 165 1954 195-204 (in Russian)
6. Kusano T. Naito M. Nonlinear oscillation for fourth order differential equations with deviating arguments Rev. Roumaine Math. Pures Appl. 23 1978 1351-1365
7. Kusano T. Naito M. On fourth order nonlinear oscillations J. London Math. Soc. 14 1976 91-105
8. Ladde G.S. Lakshmikantham V. Zhang B.G. Oscillation Theory of Differential Equations with Deviating Arguments Pure Appl. Math. 1987 Dekker New York
9. Leighton W. Nehari Z. On the oscillation of solutions of self-adjoint linear differential equations of fourth order Trans. Amer. Math. Soc. 89 1958 325-377
10. Li W.T. Positive solutions of second order nonlinear differential equations J. Math. Anal. Appl. 221 1998 326-337
11. Li W.T. Oscillation of certain second-order nonlinear differential equations J. Math. Anal. Appl. 217 1998 1-14
12. Li W.T. Fei X.L. Classifications and existence of positive solutions of higher-order nonlinear delay differential equations Nonlinear Anal. TMA 41 2000 433-445
13. Li W.T. Yan J.R. Oscillation criteria for second order superlinear differential equations Indian J. Pure Appl. Math. 28 1997 735-740
14. Li W.T. Zhang S.N. Classifications and existence of positive solutions of higher order nonlinear iterative functional equations J. Comput. Appl. Math. 139 2003 351-367
15. Li W.T. Zhong C.K. Unbounded positive solutions of higher order nonlinear functional differential equations Appl. Math. Lett. 14 2001 825-830
16. Li W.T. Huo H.F. Oscillation of the Emden-Fowler differential system Internat. J. Appl. Math. 2 2000 1453-1461
17. Li W.T. Cheng S.S. Limiting behavior of nonoscillatory solutions of a pair of coupled nonlinear differential equations Proc. Edinburgh Math. Soc. 3 2000 457-473
18. Li W.T. Fan X.L. Monotone solutions of second order nonlinear differential equations Appl. Math. Lett. 13 2000 65-70
19. Li W.T. Asymptotic behavior of nonoscillatory solutions of nth order neutral nonlinear equations with oscillating coefficients Nonlinear Anal. TMA 36 1999 891-898
20. Li W.T. Positive solutions of an odd order neutral delay nonlinear differential equation Nonlinear Anal. TMA 36 1999 899-913
21. Li W.T. Classifications and existence of nonoscillatory solutions of second order nonlinear differential equations Ann. Polon. Math. LXV 1997 283-302
22. Li W.T. Dong Z.Q. Classification and existence of positive solutions of second order nonlinear differential equations with delay depending on the unknown function, Acta Math. Sci., in press
23. Myshkis A.D. Linear Differential Equations with Retarded Arguments 1951 Gostechizdat Moscow (in Russian)
24. Norkin S.B. Differential Equations of Second Order with Retarded Arguments 1965 Nauka Moscow (in Russian)
25. Ruan J. Types and criteria of nonoscillatory solutions of second order linear neutral differential equations Chinese Ann. Math. Ser. A 8 1987 114-124 (in Chinese)
26. Terry R.D. Wong P.K. Oscillation properties of a fourth order delay differential equation Funkcial. Ekvac. 15 1972 209-220
27. Terry R.D. Oscillation properties of a fourth order delay differential equation II Funkcial. Ekvac. 16 1973 213-224
28. Wong P.J.Y. Agarwal R.P. Oscillatory behavior of solutions of certain second order nonlinear differential equations J. Math. Anal. Appl. 198 1996 337-354