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Research Article | Open Access

Non-singular solutions of p-Laplace problems, allowing multiple changes of sign in the nonlinearity

Department of Mathematical Sciences, University of Cincinnati, Cincinnati Ohio 45221-0025, USA
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Abstract

For the p-Laplace Dirichlet problem (where φ(t)=t|t|p−2, p>1)

φ(u′(x))′+f(u(x))=0for−1<x<1,u(−1)=u(1)=0

assume that f′(u)>(p−1)f(u)u>0 for u>γ>0, while ∫uγf(t)dt<0 for all u∈(0,γ). Then any positive solution, with max(−1,1)u(x)=u(0)>γ, is non-singular, no matter how many times f(u) changes sign on (0,γ). The uniqueness of solution follows.

Keywords

non-singular positive solutionsp-Laplace problems

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Electronic Research Archive
Volume 30 Issue 4,
April 2022
Pages 1414-1418
DOI: 10.3934/era.2022073

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Cite this article:
Korman P. Non-singular solutions of p-Laplace problems, allowing multiple changes of sign in the nonlinearity. Electronic Research Archive, 2022, 30(4): 1414-1418. https://doi.org/10.3934/era.2022073

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Received: 20 September 2021
Revised: 30 November 2021
Accepted: 30 November 2021
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)