Positive solution for a quasilinear equation with critical growth in ${ℝ}^N$

Lin Chen, Caisheng Chen, and Zonghu Xiu. "Positive solution for a quasilinear equation with critical growth in $ℝ^N$." Annales Polonici Mathematici 116.3 (2016): 251-262. <http://eudml.org/doc/280577>.

@article{LinChen2016,
abstract = {We study the existence of positive solutions of the quasilinear problem ⎧ $-Δ_N u + V(x)|u|^\{N-2\}u = f(u,|∇u|^\{N-2\}∇u)$, $x ∈ ℝ^N$, ⎨ ⎩ u(x) > 0, $x∈ ℝ^N$, where $Δ_N u = div(|∇u|^\{N-2\}∇u)$ is the N-Laplacian operator, $V:ℝ^N → ℝ$ is a continuous potential, $f:ℝ × ℝ^N → ℝ$ is a continuous function. The main result follows from an iterative method based on Mountain Pass techniques.},
author = {Lin Chen, Caisheng Chen, Zonghu Xiu},
journal = {Annales Polonici Mathematici},
keywords = {quasilinear problem; N-Laplacian equation; mountain pass theorem; iterative method},
language = {eng},
number = {3},
pages = {251-262},
title = {Positive solution for a quasilinear equation with critical growth in $ℝ^N$},
url = {http://eudml.org/doc/280577},
volume = {116},
year = {2016},
}

TY - JOUR
AU - Lin Chen
AU - Caisheng Chen
AU - Zonghu Xiu
TI - Positive solution for a quasilinear equation with critical growth in $ℝ^N$
JO - Annales Polonici Mathematici
PY - 2016
VL - 116
IS - 3
SP - 251
EP - 262
AB - We study the existence of positive solutions of the quasilinear problem ⎧ $-Δ_N u + V(x)|u|^{N-2}u = f(u,|∇u|^{N-2}∇u)$, $x ∈ ℝ^N$, ⎨ ⎩ u(x) > 0, $x∈ ℝ^N$, where $Δ_N u = div(|∇u|^{N-2}∇u)$ is the N-Laplacian operator, $V:ℝ^N → ℝ$ is a continuous potential, $f:ℝ × ℝ^N → ℝ$ is a continuous function. The main result follows from an iterative method based on Mountain Pass techniques.
LA - eng
KW - quasilinear problem; N-Laplacian equation; mountain pass theorem; iterative method
UR - http://eudml.org/doc/280577
ER -