Stationary Kirchhoff equations involving critical growth and vanishing potential

Marcos do Ó, João; Souto, Marco; Ubilla, Pedro

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 74.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

We establish the existence of positive solutions for a class of stationary Kirchhoff-type equations defined in the whole ℝ³ involving critical growth in the sense of the Sobolev embedding and potentials, which may decay to zero at infinity. We use minimax techniques combined with an appropriate truncated argument and a priori estimate. These results are new even for the local case, which corresponds to nonlinear Schrödinger equations.

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