| Title:
|
Nonnegativity of functionals corresponding to the second order half-linear differential equation (English) |
| Author:
|
Mařík, Robert |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
155-164 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study extremal properties of functional associated with the half–linear second order differential equation E$_p$. Necessary and sufficient condition for nonnegativity of this functional is given in two special cases: the first case is when both points are regular and the second is the case, when one end point is singular. The obtained results extend the theory of quadratic functionals. (English) |
| Keyword:
|
half–linear differential equation |
| Keyword:
|
associated functional |
| Keyword:
|
Picone identity |
| Keyword:
|
conjugate points |
| MSC:
|
34C10 |
| MSC:
|
49K15 |
| idZBL:
|
Zbl 1055.49012 |
| idMR:
|
MR1711728 |
| . |
| Date available:
|
2008-06-06T22:23:04Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107693 |
| . |
| Reference:
|
[1] Bihari, I.: On the second order half-linear differential equation.Studia Sci. Math. Hungar, 3 (1968), 411–437. Zbl 0167.37403, MR 0267190 |
| Reference:
|
[2] Došlá, Z., Došlý, O.: On transformations of singular quadratic functionals corresponding to equation $(py^{\prime })^{\prime }+qy=0$.Arch. Math. (Brno) 24 (1988), 75–82. MR 0983225 |
| Reference:
|
[3] Došlá, Z., Došlý, O.: Quadratic funtionals with general boundary conditions.Appl. Math. Opt. 36 (1997), 243–262. MR 1457870 |
| Reference:
|
[4] Elbert, Á.: A half-linear second order differential equation.Coll. Math. Soc. János Bolyai 30. Qual. theory of diff. eq. Szeged (Hungary) (1979), 153–179. |
| Reference:
|
[5] Ioffe, A. D., Tihomirov, V. M.: Theory of extremal problems.North-Holland Publ., 1979, pp. 122–124. MR 0528295 |
| Reference:
|
[6] Jaroš, J., Kusano, T.: A Picone type identity for second order half-linear differential equations.(to appear). MR 1711081 |
| Reference:
|
[7] Kaňovský, J.: Global transformations of linear differential equations and quadratic functionals I,II.Arch. Math. 19 (1983), 161–171. MR 0725199 |
| Reference:
|
[8] Leighton, W., Morse, M.: Singular quadratic functionals.Trans. Amer. Math. Soc. 40 (1936), 252–286. MR 1501873 |
| Reference:
|
[9] Li, H. J., Yeh, Ch. Ch.: Sturmian comparison theorem for half-linear second order diff. equations.Proc. Roy. Soc. of Edinburg 125 A (1995), 1193–1204. MR 1362999 |
| Reference:
|
[10] Reid, W. T.: Ordinary differential equations.John Wiley and Sons, New York, 1971. Zbl 0212.10901, MR 0273082 |
| . |
