Some nodal properties for a quasilinear differential equation involving the p-Laplacian

In this paper, we study a quasilinear differential equation(|u′(x)|p−2u′(x))′+w(x)|u(x)|q−2u(x)=0in(0,b), where q>p>1. A theorem related to some oscillation properties depending on the initial parameters is developed. On the basis of this result, we also show that the identical zero set of sol...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-04, Vol.472 (1), p.1093-1105
Main Author: Wang, Wei-Chuan
Format: Article
Language:English
Subjects:
Nonlinear p-Laplacian equation
Sign-changing solution
Uniqueness
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Summary:In this paper, we study a quasilinear differential equation(|u′(x)|p−2u′(x))′+w(x)|u(x)|q−2u(x)=0in(0,b), where q>p>1. A theorem related to some oscillation properties depending on the initial parameters is developed. On the basis of this result, we also show that the identical zero set of solutions will determine the function w(x) uniquely under some minor assumption. Essentially, the main methods using in this work are the scaling argument and Prüfer-type substitutions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.11.066