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

• Autorzy: Honghui Yin , Zuodong Yang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35J50: Variational methods for elliptic systems
• 35J47: Second-order elliptic systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2011
• Tom: 102
• Numer: 1
• Strony: 51-71

Daty

wydano

2011

Twórcy

autor

Honghui Yin

• Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210046, China
• School of Mathematical Sciences, Huaiyin Normal University, Huaian, Jiangsu 223001, China

autor

Zuodong Yang

• Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210046, China
• College of Zhongbei, Nanjing Normal University, Nanjing, Jiangsu 210046, China

Identyfikatory

DOI

10.4064/ap102-1-5