Existence Results for a Class of Semilinear Elliptic Systems

• 来源期刊: 偏微分方程(英文版)
• 学科: 数学
• 关键词: Elliptic systems homotopy topological degree
• 年，卷（期）: 2009,（2）
• 页码范围: 111-126
• 页数: 16页
• 分类号: O175.25|O175.29
• 语种: 英文

摘要

In this paper, we study the existence of nontrivial solutions for the problem-△u=∫(x,u,v)+h1(x)inΩ -△v=g(x,u,v)h2(x)inΩ u=v=0 oneΩwhere Ω is bounded domain in RN and h1,h2 ∈L2 (Ω). The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities ∫ and g: s,|t|→+∞lim ∫(x,s,t)/s=s|,t|→+∞lim g(x,s,t)/t=λ+, unifrmly onΩ, -s,|t|→+∞lim ∫(x,s,t)/s=s|,t|→+∞lim g(x,s,t)/t=λ-, unifrmly onΩ,where λ+,λ-∈{0}∪σ(-△),σ(-△) denote the spectrum of-△. The cases (i) where λ+=λ- and (ii) where λ+=λ- such that the closed interval with endpoints λ+,λ- contains at most one simple eigenvalue of -△ are considered.