Keywords: half-linear differential equation; conjugacy criteria; variational principle; energy functional; half-linear trigonometric functions
@article{10_5817_AM2013_1_9,
author = {Chv\'atal, Martin and Do\v{s}l\'y, Ond\v{r}ej},
title = {Variational method and conjugacy criteria for half-linear differential equations},
journal = {Archivum mathematicum},
pages = {9--16},
year = {2013},
volume = {49},
number = {1},
doi = {10.5817/AM2013-1-9},
mrnumber = {3073011},
zbl = {06321143},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2013-1-9/}
}
TY - JOUR AU - Chvátal, Martin AU - Došlý, Ondřej TI - Variational method and conjugacy criteria for half-linear differential equations JO - Archivum mathematicum PY - 2013 SP - 9 EP - 16 VL - 49 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.5817/AM2013-1-9/ DO - 10.5817/AM2013-1-9 LA - en ID - 10_5817_AM2013_1_9 ER -
Chvátal, Martin; Došlý, Ondřej. Variational method and conjugacy criteria for half-linear differential equations. Archivum mathematicum, Tome 49 (2013) no. 1, pp. 9-16. doi: 10.5817/AM2013-1-9
[1] Abd–Alla, M. Z., Abu–Risha, M. H.: Conjugacy criteria for the half–linear second order differential equation. Rocky Mountain J. Math. 38 (2008), 359–372. | DOI | MR | Zbl
[2] Chantladze, T., Kandelaki, N., Lomtatidze, A.: On zeros of solutions of a second order singular half-linear equation. Mem. Differential Equations Math. Phys. 17 (1999), 127–154. | MR
[3] Chantladze, T., Lomtatidze, A., Ugulava, D.: Conjugacy and disconjugacy criteria for second order linear ordinary differential equations. Arch. Math. (Brno) 36 (2000), 313–323. | MR | Zbl
[4] Došlý, O.: Conjugacy criteria for second order differential equations. Rocky Mountain. J. Math. 23 (1993), 849–861. | DOI | MR
[5] Došlý, O.: A remark on conjugacy of half–linear second order differential equations. Math. Slovaca 50 (2000), 67–79. | MR | Zbl
[6] Došlý, O., Elbert, Á.: Conjugacy of half–linear second order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 130 (2000), 517–525. | MR | Zbl
[7] Došlý, O., Řehák, P.: Half-Linear Differential Equations. North-Holland Mathematics Studies, vol. 202, Elsevier Science B.V., Amsterdam, 2005. | MR | Zbl
[8] Elbert, Á.: A half–linear second order differential equation. Colloq. Math. Soc. János Bolyai 30 (1979), 158–180.
[9] Kumari, Sowjanaya I., Umamaheswaram, S.: Oscillation criteria for linear matrix Hamiltonian systems. J. Differential Equations 165 (2000), 174–198. | DOI | MR
[10] Lomtatidze, A.: Existence of conjugate points for second-order linear differential equations. Georgian Math. J. 2 (1995), 93–98. | DOI | MR | Zbl
[11] Mařík, R.: A remark on connection between conjugacy of half-linear differential equation and equation with mixed nonlinearities. Appl. Math. Lett. 24 (2011), 93–96. | DOI | MR | Zbl
[12] Müller–Pfeiff, E., Schott, Th.: On the existence of conjugate points for Sturm–Liouville differential equations. Z. Anal. Anwendungen 9 (1990), 155–164. | MR
[13] Müller–Pfeiffer, E.: Existence of conjugate points for second and fourth order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 89 (1981), 281–291. | MR | Zbl
[14] Müller–Pfeiffer, E.: On the existence of conjugate points for Sturm–Liouville equations on noncompact intervals. Math. Nachr. 152 (1991), 49–57. | DOI | MR
[15] Peña, S.: Conjugacy criteria for half–linear differential equations. Arch. Math. (Brno) 35 (1999), 1–11. | MR | Zbl
[16] Tipler, F. J.: General relativity and conjugate ordinary differential equations. J. Differential Equations 30 (1978), 165–174. | DOI | MR | Zbl
Cité par Sources :