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.
Cite this article
Giovany M. Figueiredo, Antonio Suárez, Some remarks on the comparison principle in Kirchhoff equations. Rev. Mat. Iberoam. 34 (2018), no. 2, pp. 609–620DOI 10.4171/RMI/997