| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 74 | |
| Number of page(s) | 19 | |
| DOI | https://doi.org/10.1051/cocv/2019054 | |
| Published online | 30 September 2020 | |
Stationary Kirchhoff equations involving critical growth and vanishing potential*
1
Department of Mathematics, Federal University of Paraíba,
58051-900
João Pessoa-PB, Brazil.
2
Unidade Acadêmica de Matemática e Estatística, Federal University of Campina Grande,
58109-970
Campina Grande-PB, Brazil.
3
Departamento de Matemática y C.C., Universidad de Santiago de Chile, Casilla 307, Correo 2,
Santiago, Chile.
** Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
3
February
2019
Accepted:
28
August
2019
Abstract
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.
Mathematics Subject Classification: 35J20 / 35J60 / 35B33
Key words: Kirchhoff-type equation / nonlinear Schrödinger equation / critical exponent / variational method / vanishing potentials / compactness
Research supported in part by INCTmat/MCT/Brazil, CNPq and CAPES/Brazil, FONDECYT 1181125.
© EDP Sciences, SMAI 2020
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