Multiplicity results for a class of concave-convex elliptic systems involving sign-changing weight functions

Honghui Yin, and Zuodong Yang. "Multiplicity results for a class of concave-convex elliptic systems involving sign-changing weight functions." Annales Polonici Mathematici 102.1 (2011): 51-71. <http://eudml.org/doc/280861>.

@article{HonghuiYin2011,
abstract = {Our main purpose is to establish the existence of weak solutions of second order quasilinear elliptic systems ⎧ $-Δ_pu + |u|^\{p-2\}u = f_\{1λ₁\}(x) |u|^\{q-2\}u + 2α/(α+β) g_μ|u|^\{α-2\} u|v|^β$, x ∈ Ω, ⎨ $-Δ_pv + |v|^\{p-2\}v = f_\{2λ₂\}(x) |v|^\{q-2\}v + 2β/(α+β) g_μ|u|^α|v|^\{β-2\}v$, x ∈ Ω, ⎩ u = v = 0, x∈ ∂Ω, where 1 < q < p < N and $Ω ⊂ ℝ^N$ is an open bounded smooth domain. Here λ₁, λ₂, μ ≥ 0 and $f_\{iλ_i\}(x) = λ_if_\{i+\}(x) + f_\{i-\}(x)$ (i = 1,2) are sign-changing functions, where $f_\{i±\}(x) = max\{±f_i(x),0\}$, $g_μ(x) = a(x) + μb(x)$, and $Δ_p u = div(|∇u|^\{p-2\}∇u)$ denotes the p-Laplace operator. We use variational methods.},
author = {Honghui Yin, Zuodong Yang},
journal = {Annales Polonici Mathematici},
keywords = {bounded Nehari manifold; positive solution; sequence; weak solutions; second-order quasilinear elliptic systems},
language = {eng},
number = {1},
pages = {51-71},
title = {Multiplicity results for a class of concave-convex elliptic systems involving sign-changing weight functions},
url = {http://eudml.org/doc/280861},
volume = {102},
year = {2011},
}

TY - JOUR
AU - Honghui Yin
AU - Zuodong Yang
TI - Multiplicity results for a class of concave-convex elliptic systems involving sign-changing weight functions
JO - Annales Polonici Mathematici
PY - 2011
VL - 102
IS - 1
SP - 51
EP - 71
AB - Our main purpose is to establish the existence of weak solutions of second order quasilinear elliptic systems ⎧ $-Δ_pu + |u|^{p-2}u = f_{1λ₁}(x) |u|^{q-2}u + 2α/(α+β) g_μ|u|^{α-2} u|v|^β$, x ∈ Ω, ⎨ $-Δ_pv + |v|^{p-2}v = f_{2λ₂}(x) |v|^{q-2}v + 2β/(α+β) g_μ|u|^α|v|^{β-2}v$, x ∈ Ω, ⎩ u = v = 0, x∈ ∂Ω, where 1 < q < p < N and $Ω ⊂ ℝ^N$ is an open bounded smooth domain. Here λ₁, λ₂, μ ≥ 0 and $f_{iλ_i}(x) = λ_if_{i+}(x) + f_{i-}(x)$ (i = 1,2) are sign-changing functions, where $f_{i±}(x) = max{±f_i(x),0}$, $g_μ(x) = a(x) + μb(x)$, and $Δ_p u = div(|∇u|^{p-2}∇u)$ denotes the p-Laplace operator. We use variational methods.
LA - eng
KW - bounded Nehari manifold; positive solution; sequence; weak solutions; second-order quasilinear elliptic systems
UR - http://eudml.org/doc/280861
ER -