Wirtinger inequality and nonlinear differential systems

Jaroslav Jaroš

Archivum Mathematicum (2013)

  • Volume: 049, Issue: 1, page 35-41
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Jaroš, Jaroslav. "Wirtinger inequality and nonlinear differential systems." Archivum Mathematicum 049.1 (2013): 35-41. <http://eudml.org/doc/252508>.

@article{Jaroš2013,
abstract = {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.},
author = {Jaroš, Jaroslav},
journal = {Archivum Mathematicum},
keywords = {nonlinear differential system; Picone identity; Wirtinger inequality; nonlinear differential system; Picone identity; Wirtinger inequality},
language = {eng},
number = {1},
pages = {35-41},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Wirtinger inequality and nonlinear differential systems},
url = {http://eudml.org/doc/252508},
volume = {049},
year = {2013},
}

TY - JOUR
AU - Jaroš, Jaroslav
TI - Wirtinger inequality and nonlinear differential systems
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 1
SP - 35
EP - 41
AB - 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.
LA - eng
KW - nonlinear differential system; Picone identity; Wirtinger inequality; nonlinear differential system; Picone identity; Wirtinger inequality
UR - http://eudml.org/doc/252508
ER -

References

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  1. Elbert, Á., A half-linear second order differential equation, Colloq. Math. János Bolyai 30 (1979), 153–180. (1979) MR0680591
  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. (1997) 
  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. (1999) Zbl0926.34023MR1711081
  4. Kreith, K., 10.1016/0022-247X(70)90024-7, J. Math. Anal. Appl. 31 (1970), 297–308. (1970) MR0261088DOI10.1016/0022-247X(70)90024-7
  5. Kreith, K., A class of comparison theorems for nonselfadjoint elliptic equations, Proc. Amer. Math. Soc. 29 (1971), 547–552. (1971) Zbl0231.35021MR0279418
  6. Kreith, K., Oscillation theory, Lecture Notes in Math., vol. 324, Springer, 1973. (1973) Zbl0258.35001
  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. (1995) MR1362999
  8. Mirzov, J. D., 10.1016/0022-247X(76)90120-7, J. Math. Anal. Appl. 53 (1976), 418–425. (1976) Zbl0327.34027MR0402184DOI10.1016/0022-247X(76)90120-7
  9. Wong, P. K., A Sturmian theorem for first order partial differential equations, Trans. Amer. Math. Soc. 166 (1972), 126–131. (1972) Zbl0238.35013MR0294911
  10. Yoshida, N., Oscillation Theory of Partial Differential Equations, World Scientific, Singapore, Hackensack, London, 2008. (2008) Zbl1154.35001MR2485076

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