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Oscillation of a class of differential equations with generalized phi-Laplacian

Published online by Cambridge University Press:  22 May 2013

Mariella Cecchi ,
Zuzana Došlá  and
Mauro Marini
Mariella Cecchi
Affiliation:
Department of Electronics and Telecommunications, University of Florence, 50139 Florence, Italy (mariella.cecchi@unifi.it)
Zuzana Došlá
Affiliation:
Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic (dosla@math.muni.cz)
Mauro Marini
Affiliation:
Department of Mathematics and Informatics ‘Ulisse Dini’, University of Florence, 50139 Florence, Italy (mauro.marini@unifi.it)
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Abstract

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The oscillation of the nonlinear differential equation

where Φ is an increasing odd homeomorphism, is considered when the weight b is not summable near infinity. We extend previous results, stated for equations with the classical p-Laplacian, by obtaining necessary and sufficient conditions of integral type for the oscillation. The role of the boundedness of Im Φ [Dom Φ] is analysed in detail. Our results includes the case Φ* ◦ F linear near zero or near infinity, where Φ* is the inverse of Φ. Several examples, concerning the curvature or relativity operator, illustrate our results.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 3 , June 2013 , pp. 493 - 506
Copyright
Copyright © Royal Society of Edinburgh 2013