Limit-point type solutions of nonlinear differential equations

Journal of Mathematical Analysis and Applications

Volumn 294, Issue 2, 2004, Pages 548-559

  Mustafa, Octavian G ^a   Rogovchenko, Yuri V ^b  

^a UNIVERSITY OF CRAIOVA   (Romania)

^b EASTERN MEDITERRANEAN UNIVERSITY   (Turkey)

Author keywords

Limit point limit circle classification; Nonlinear differential equations; Second order; Square integrable solutions

Indexed keywords

EID: 3142747522     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.02.029     Document Type: Article

References (28)

1. Atkinson F.V. Nonlinear extensions of limit-point criteria Math. Z. 130 1973 297-312
2. Bartušek M. Graef J.R. On the limit-point/limit-circle problem for second order nonlinear equations Nonlinear Stud. 9 2002 361-369
3. Bartušek M. Došlá Z. Graef J.R. Nonlinear limit-point type solutions of nth order differential equations J. Math. Anal. Appl. 209 1997 122-139
4. Bartušek M. Došlá Z. Graef J.R. On the definitions of the nonlinear limit-point/limit-circle properties Differential Equations Dynam. Systems 9 2001 49-61
5. Bartušek M. Došlá Z. Graef J.R. The nonlinear limit-point/limit-circle problem for higher order equations, Equadiff 9 (Brno, 1997), Arch. Math. (Brno) 34 1998 13-22
6. 2-solutions of a class of nonlinear differential equations Proc. Edinburgh Math. Soc. (2) 14 1965 257-268
7. Coddington E.A. Levinson N. Theory of Ordinary Differential Equations 1955 McGraw-Hill New York
8. p(0,∞) Math. Balkanica 4 1974 115-119 (in Russian)
9. 2(0,∞) Math. Slovaca 32 1982 427-434
10. Graef J.R. Limit-circle criteria and related problems for nonlinear equations J. Differential Equations 35 1980 319-338
11. Graef J.R. Spikes P.W. On the nonlinear limit-point/limit-circle problem Nonlinear Anal. 7 1983 851-871
12. Graef J.R. Spikes P.W. On the nonoscillation, convergence to zero, and integrability of solutions of a second order nonlinear differential equation Math. Nachr. 130 1987 139-149
13. 2-solutions of nth order differential equations Proc. Edinburgh Math. Soc. (2) 24 1981 131-136
14. p-solutions of certain nonlinear differential equations Glasgow Math. J. 8 1967 133-138
15. Hallam T.G. Asymptotic integration of second order differential equations with integrable coefficients SIAM J. Appl. Math. 19 1970 430-439
16. Hartman P. Wintner A. On non-oscillatory linear differential equations Amer. J. Math. 75 1953 717-730
17. Kauffman R.M. Thomas T. Zettl A. The Deficiency Index Problem for Powers of Ordinary Differential Expressions Lecture Notes in Mathematics vol. 621 1977 Springer-Verlag Berlin
18. Mustafa O.G. Rogovchenko Yu.V. Global existence of solutions with prescribed asymptotic behavior for second-order nonlinear differential equations Nonlinear Anal. 51 2002 339-368
19. Mustafa O.G. Rogovchenko Yu.V. Existence of square integrable solutions of perturbed nonlinear differential equations, Proc. Fourth Internat. Conf. Dynam. Systems Differential Equations, Discrete Contin. Dynam. Systems supplement volume 2003 647-655
20. Mustafa O.G. Rogovchenko Yu.V. Limit-point type results for linear differential equations Arch. Inequal. Appl. 1 2003 387-395
21. Mustafa O.G. Rogovchenko Yu.V. Limit-point criteria for superlinear differential equations Bull. Belg. Math. Soc. Simon Stevin 2004 in press
22. Patula W.T. Waltman P. Limit point classification of second order linear differential equations J. London Math. Soc. (2) 8 1974 209-216
23. Suyemoto L. Waltman P. Extension of a theorem of A. Wintner Proc. Amer. Math. Soc. 14 1963 970-971
24. Weyl H. Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörige Entwocklungen willkülricher Funktionen Math. Ann. 68 1910 220-269
25. 2)-solutions of a non-oscillatory differential equation J. London Math. Soc. 25 1950 347-351
26. Wong J.S.W. Remarks on a theorem of A. Wintner Enseign. Math. (2) 13 1967 103-106
27. 2-solutions of linear ordinary differential equations Duke Math. J. 38 1971 93-97
28. Zettl A. Square integrable solutions of Ly=f(t,y) Proc. Amer. Math. Soc. 26 1970 635-639