| Title:
|
Variational method and conjugacy criteria for half-linear differential equations (English) |
| Author:
|
Chvátal, Martin |
| Author:
|
Došlý, Ondřej |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
9-16 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We establish new conjugacy criteria for half-linear second order differential equations. These criteria are based on the relationship between conjugacy of the investigated equation and nonpositivity of the associated energy functional. (English) |
| Keyword:
|
half-linear differential equation |
| Keyword:
|
conjugacy criteria |
| Keyword:
|
variational principle |
| Keyword:
|
energy functional |
| Keyword:
|
half-linear trigonometric functions |
| MSC:
|
34A34 |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 06321143 |
| idMR:
|
MR3073011 |
| DOI:
|
10.5817/AM2013-1-9 |
| . |
| Date available:
|
2013-05-28T13:25:07Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143295 |
| . |
| Reference:
|
[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. Zbl 1195.34048, MR 2401558, 10.1216/RMJ-2008-38-2-359 |
| Reference:
|
[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 1710580 |
| Reference:
|
[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. Zbl 1054.34053, MR 1811176 |
| Reference:
|
[4] Došlý, O.: Conjugacy criteria for second order differential equations.Rocky Mountain. J. Math. 23 (1993), 849–861. MR 1245450, 10.1216/rmjm/1181072527 |
| Reference:
|
[5] Došlý, O.: A remark on conjugacy of half–linear second order differential equations.Math. Slovaca 50 (2000), 67–79. Zbl 0959.34025, MR 1764346 |
| Reference:
|
[6] Došlý, O., Elbert, Á.: Conjugacy of half–linear second order differential equations.Proc. Roy. Soc. Edinburgh Sect. A 130 (2000), 517–525. Zbl 0961.34020, MR 1769240 |
| Reference:
|
[7] Došlý, O., Řehák, P.: Half-Linear Differential Equations.North-Holland Mathematics Studies, vol. 202, Elsevier Science B.V., Amsterdam, 2005. Zbl 1090.34001, MR 2158903 |
| Reference:
|
[8] Elbert, Á.: A half–linear second order differential equation.Colloq. Math. Soc. János Bolyai 30 (1979), 158–180. |
| Reference:
|
[9] Kumari, Sowjanaya I., Umamaheswaram, S.: Oscillation criteria for linear matrix Hamiltonian systems.J. Differential Equations 165 (2000), 174–198. MR 1771793, 10.1006/jdeq.1999.3746 |
| Reference:
|
[10] Lomtatidze, A.: Existence of conjugate points for second-order linear differential equations.Georgian Math. J. 2 (1995), 93–98. Zbl 0820.34018, MR 1310503, 10.1007/BF02257736 |
| Reference:
|
[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. Zbl 1214.34031, MR 2735120, 10.1016/j.aml.2010.08.024 |
| Reference:
|
[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 1063251 |
| Reference:
|
[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. Zbl 0481.34019, MR 0635764 |
| Reference:
|
[14] Müller–Pfeiffer, E.: On the existence of conjugate points for Sturm–Liouville equations on noncompact intervals.Math. Nachr. 152 (1991), 49–57. MR 1121223, 10.1002/mana.19911520106 |
| Reference:
|
[15] Peña, S.: Conjugacy criteria for half–linear differential equations.Arch. Math. (Brno) 35 (1999), 1–11. Zbl 1054.34055, MR 1684518 |
| Reference:
|
[16] Tipler, F. J.: General relativity and conjugate ordinary differential equations.J. Differential Equations 30 (1978), 165–174. Zbl 0362.34023, MR 0513268, 10.1016/0022-0396(78)90012-8 |
| . |
