Volume 26, 2020
|Number of page(s)||19|
|Published online||30 September 2020|
Stationary Kirchhoff equations involving critical growth and vanishing potential*
Department of Mathematics, Federal University of Paraíba,
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: firstname.lastname@example.org
Accepted: 28 August 2019
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
© EDP Sciences, SMAI 2020
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