Geodesic
Wirtinger inequality and nonlinear differential systems
Archivum mathematicum, Tome 49 (2013) no. 1, pp. 35-41 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.5817/AM2013-1-35
Classification : 34A05, 34C10
Keywords: nonlinear differential system; Picone identity; Wirtinger inequality 
@article{10_5817_AM2013_1_35,
     author = {Jaro\v{s}, Jaroslav},
     title = {Wirtinger inequality and nonlinear differential systems},
     journal = {Archivum mathematicum},
     pages = {35--41},
     year = {2013},
     volume = {49},
     number = {1},
     doi = {10.5817/AM2013-1-35},
     mrnumber = {3073014},
     zbl = {06321146},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2013-1-35/}
}
TY  - JOUR
AU  - Jaroš, Jaroslav
TI  - Wirtinger inequality and nonlinear differential systems
JO  - Archivum mathematicum
PY  - 2013
SP  - 35
EP  - 41
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2013-1-35/
DO  - 10.5817/AM2013-1-35
LA  - en
ID  - 10_5817_AM2013_1_35
ER  - 
%0 Journal Article
%A Jaroš, Jaroslav
%T Wirtinger inequality and nonlinear differential systems
%J Archivum mathematicum
%D 2013
%P 35-41
%V 49
%N 1
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2013-1-35/
%R 10.5817/AM2013-1-35
%G en
%F 10_5817_AM2013_1_35
Jaroš, Jaroslav. Wirtinger inequality and nonlinear differential systems. Archivum mathematicum, Tome 49 (2013) no. 1, pp. 35-41. doi: 10.5817/AM2013-1-35

[1] Elbert, Á.: A half-linear second order differential equation. Colloq. Math. János Bolyai 30 (1979), 153–180. | MR

[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.

[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. | MR | Zbl

[4] Kreith, K.: A Picone identity for first order systems. J. Math. Anal. Appl. 31 (1970), 297–308. | DOI | MR

[5] Kreith, K.: A class of comparison theorems for nonselfadjoint elliptic equations. Proc. Amer. Math. Soc. 29 (1971), 547–552. | MR | Zbl

[6] Kreith, K.: Oscillation theory. Lecture Notes in Math., vol. 324, Springer, 1973. | Zbl

[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

[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. | DOI | MR | Zbl

[9] Wong, P. K.: A Sturmian theorem for first order partial differential equations. Trans. Amer. Math. Soc. 166 (1972), 126–131. | MR | Zbl

[10] Yoshida, N.: Oscillation Theory of Partial Differential Equations. World Scientific, Singapore, Hackensack, London, 2008. | MR | Zbl

Cité par Sources :