Existence and asymptotic behavior of positive solutions for elliptic systems with nonstandard growth conditions

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

Abstrakty

EN

Our main purpose is to establish the existence of a positive solution of the system
⎧$-∆_{p(x)}u = F(x,u,v)$, x ∈ Ω,
⎨$-∆_{q(x)}v = H(x,u,v)$, x ∈ Ω,
⎩u = v = 0, x ∈ ∂Ω,
where $Ω ⊂ ℝ^{N}$ is a bounded domain with C² boundary, $F(x,u,v) = λ^{p(x)}[g(x)a(u) + f(v)]$, $H(x,u,v) = λ^{q(x})[g(x)b(v) + h(u)]$, λ > 0 is a parameter, p(x),q(x) are functions which satisfy some conditions, and $-∆_{p(x)}u = -div(|∇u|^{p(x)-2}∇u)$ is called the p(x)-Laplacian. We give existence results and consider the asymptotic behavior of solutions near the boundary. We do not assume any symmetry conditions on the system.

Kategorie tematyczne

• 35J60: Nonlinear elliptic equations
• 35J25: Boundary value problems for second-order elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2012
• Tom: 104
• Numer: 3
• Strony: 293-308

Daty

wydano

2012

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/ap104-3-6