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Some remarks on the comparison principle in Kirchhoff equations

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arxiv 1510.02151 v1 pith:CWZMU7MW submitted 2015-10-07 math.AP

Giovany M. Figueiredo , Antonio Suarez This is my paper · ORCID
classification math.AP
keywords kirchhoffsomecomparisonequationsmethodprinciplesub-supersolutionalternative
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In this paper we study the validity of the comparison principle and the sub-supersolution method for Kirchhoff type equations. We show that these principles do not work when the Kirchhoff function is increasing, contradicting some previous results. We give an alternative sub-supersolution method and apply it to some models.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An iterative method for Kirchhoff type equations and its applications

    math.AP 2019-08 reject novelty 6.0 of 10

    An invariant-set existence theorem for nonlocal Kirchhoff-Carrier equations is asserted, but the proof rests on a false identity for r_M and an invalid gradient bound.

  2. Positive solutions of inhomogeneous Kirchhoff type equations with indefinite data

    math.AP 2019-08 conditional novelty 5.0 of 10

    For a Kirchhoff equation with indefinite data, the paper characterizes positive solvability through an auxiliary linear problem, showing existence, multiplicity, uniqueness, and nonexistence depending on the exponent ...

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