Methods of oscillation theory of half-linear second order differential equations

Czechoslovak Mathematical Journal

Volumn 50, Issue 3, 2000, Pages 657-671

  Došlý, Ondřej ^a  

^a MATHEMATICAL INSTITUTE   (Czech Republic)

Author keywords

Half linear equation; Oscillation and nonoscillation criteria; Principal solution; Reciprocity principle; Riccati technique; Variational principle

Indexed keywords

EID: 0035648175     PISSN: 00114642     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022854131381     Document Type: Article

References (22)

1. C. D. Ahlbrandt: Equivalent boundary value problems for self-adjoint differential systems. J. Differential Equations 9 (1971), 420-435.
2. C. D. Ahlbrandt: Principal and antiprincipal solutions of self-adjoint differential systems and their reciprocals. Rocky Mountain J. Math. 2 (1972), 169-189.
3. p-2x = 0, p > 1. Houston J. Math. 77(1991), 63-70.
4. O. Došlý: Oscillation criteria for half-linear second order differential equations. Hiroshima J. Math. 28 (1998), 507-521.
5. O. Došlý: A remark on conjugacy of half-linear second order differential equations. Math. Slovaca 2000. To appear.
6. O. Došlý: Principal solutions and transformations of linear Hamiltonian systems. Arch. Math. 28 (1992), 113-120.
7. O. Došlý, A. Lomtatidze: Oscillation and nonoscillation criteria for half-linear second order differential equations. To appear in Ann. Polon. Math.
8. Á. Elbert: A half-linear second order differential equation. Colloq. Math. Soc. János Bolyai 30 (1979), 158-180.
9. Á. Elbert: Oscillation and nonoscillation theorems for some non-linear ordinary differential equations. Lecture Notes in Math. 964 (1982), 187-212.
10. Á. Elbert: Asymptotic behaviour of autonomous half-linear differential systems on the plane. Studia Sci. Math. Hungar. 19 (1984), 447-464.
11. Á. Elbert, T. Kusano: Principal solutions of nonoscillatory half-linear differential equations. Adv. Math. Sci. Appl. 18 (1998), 745-759.
12. E. Hille: Nonoscillation theorems. Trans. Amer. Math. Soc. 64 (1948), 234-252.
13. J. Jaroš, T. Kusano: A Picone type identity for half-linear differential equations. Acta Math. Univ. Comen. 68 (1999), 137-151.
14. T. Kusano, Y. Naito: Oscillation and nonoscillation criteria for second order quasilinear differential equations. Acta Math. Hungar. 76 (1997), 81-99.
15. T. Kusano, Y. Naito, A. Ogata: Strong oscillation and nonoscillation of quasilinear differential equations of second order. Differential Equations Dynam. Systems 2 (1994), 1-10.
16. H. J. Li: Oscillation criteria for half-linear second order differential equations. Hiroshima Math. J. 25 (1995), 571-583.
17. H. J. Li, C. C. Yeh: Sturmian comparison theorem for half-linear second order differential equations. Proc. Roy. Soc. Edinburgh 125A (1996), 1193-1204.
18. A. Lomtatidze: Oscillation and nonoscillation of Emden-Fowler type equation of second order. Arch. Math. 32 (1996), 181-193.
19. R. Mařík: Nonnegativity of functional corresponding to the second order half-linear differential equation, submitted.
20. J. D. Mirzov: On some analogs of Sturm's and Kneser's theorems for nonlinear systems. J. Math. Anal. Appl. 53 (1976), 418-425.
21. J. D. Mirzov: Principal and nonprincipal solutions of a nonoscillatory system. Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 31 (1988), 100-117.
22. A. Wintner: On the non-existenae of conjugate points. Amer. J. Math. 73 (1951), 368-380.