| Title:
|
Wirtinger inequality and nonlinear differential systems (English) |
| Author:
|
Jaroš, Jaroslav |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
35-41 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Picone identity for a class of nonlinear differential equations is established and various qualitative results (such as Wirtinger-type inequality and the existence of zeros of first components of solutions) are obtained with the help of this new formula. (English) |
| Keyword:
|
nonlinear differential system |
| Keyword:
|
Picone identity |
| Keyword:
|
Wirtinger inequality |
| MSC:
|
34A05 |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 06321146 |
| idMR:
|
MR3073014 |
| DOI:
|
10.5817/AM2013-1-35 |
| . |
| Date available:
|
2013-05-28T13:28:42Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143298 |
| . |
| Reference:
|
[1] Elbert, Á.: A half-linear second order differential equation.Colloq. Math. János Bolyai 30 (1979), 153–180. MR 0680591 |
| Reference:
|
[2] Jaroš, J., Kusano, T.: On forced second order half–linear equations.Proceedings of the Symposium on the Structure and Methods of Functional Differential Equations, RIMS, Kokyuroku 984, Kyoto University, 1997, in Japanese, pp. 191–197. |
| Reference:
|
[3] Jaroš, J., Kusano, T.: A Picone–type identity for second order half–linear differential equations.Acta Math. Univ. Comenian. (N.S.) 68 (1999), 137–151. Zbl 0926.34023, MR 1711081 |
| Reference:
|
[4] Kreith, K.: A Picone identity for first order systems.J. Math. Anal. Appl. 31 (1970), 297–308. MR 0261088, 10.1016/0022-247X(70)90024-7 |
| Reference:
|
[5] Kreith, K.: A class of comparison theorems for nonselfadjoint elliptic equations.Proc. Amer. Math. Soc. 29 (1971), 547–552. Zbl 0231.35021, MR 0279418 |
| Reference:
|
[6] Kreith, K.: Oscillation theory.Lecture Notes in Math., vol. 324, Springer, 1973. Zbl 0258.35001 |
| Reference:
|
[7] Li, H. J., Yeh, C. C.: Surmian comparison theorem for half–linear second order differential equations.Proc. Roy. Soc. Edinburgh 125A (1995), 1193–1204. MR 1362999 |
| Reference:
|
[8] Mirzov, J. D.: On some analogs of Sturm’s and Kneser’s theorems for nonlinear systems.J. Math. Anal. Appl. 53 (1976), 418–425. Zbl 0327.34027, MR 0402184, 10.1016/0022-247X(76)90120-7 |
| Reference:
|
[9] Wong, P. K.: A Sturmian theorem for first order partial differential equations.Trans. Amer. Math. Soc. 166 (1972), 126–131. Zbl 0238.35013, MR 0294911 |
| Reference:
|
[10] Yoshida, N.: Oscillation Theory of Partial Differential Equations.World Scientific, Singapore, Hackensack, London, 2008. Zbl 1154.35001, MR 2485076 |
| . |
