@misc{10481/59925,
year = {2019},
url = {http://hdl.handle.net/10481/59925},
abstract = {In this paper, we study the existence of viscosity solutions to the Gelfand problem for the 1-homogeneous
p-Laplacian in a bounded domain Ω ⊂ ℝN, that is, we deal with
− 1
p − 1|∇u|2−p div(|∇u|p−2∇u) = λeu
in Ω with u = 0 on ∂Ω. For this problem we show that, for p ∈ [2, ∞], there exists a positive critical value
λ∗ = λ∗(Ω, N, p) such that the following holds:
∙ If λ < λ∗, the problem admits a minimal positive solution wλ.
∙ If λ > λ∗, the problem admits no solution.
Moreover, the branch of minimal solutions {wλ} is increasing with λ. In addition, using degree theory, for
fixed p we show that there exists an unbounded continuum of solutions that emanates from the trivial solution
u = 0 with λ = 0, and for a small fixed λ we also obtain a continuum of solutions with p ∈ [2, ∞].},
organization = {The first author was partially supported by MINECO–FEDER Grant MTM2015-68210-P (Spain)
and Junta de Andalucía FQM-194 (Spain). The second author was partially supported by MINECO–FEDER
Grant MTM2015-68210-P (Spain), Junta de Andalucía FQM-116 (Spain) and MINECO Grant BES-2013-
066595 (Spain). The third author was partially supported by CONICET (Argentina) and MINECO–FEDER
Grant MTM2015-70227-P (Spain).},
publisher = {Walter de Gruyter GmbH},
keywords = {Gelfand problem},
keywords = {Elliptic equations},
keywords = {Viscosity solutions},
title = {The Gelfand problem for the 1-homogeneous p-Laplacian},
doi = {10.1515/anona-2016-0233},
author = {Carmona Tapia, José and Molino Salas, Alexis and Rossi, Julio D.},
}