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

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Authors

CECCHI Mariella DOŠLÁ Zuzana MARINI Mauro

Year of publication 2013
Type Article in Periodical
Magazine / Source Proc. Roy. Soc. Edinburgh
MU Faculty or unit

Faculty of Science

Citation
Web http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8924889
Doi http://dx.doi.org/10.1017/S0308210511001156
Field General mathematics
Keywords Oscillation; Phi-Laplacian; integral oscillation conditions
Description Oscillation of a certain nonlinear differential equation involving the so called Phi-Laplacian - an increasing odd homeomorphism, is considered. 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 Phi [Dom Phi] is analysed in detail. Our results includes the case Phi*(Phi) linear near zero or near infinity, where Phi* is the inverse of Phi. Several examples, concerning the curvature or relativity operator, illustrate our results.
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