AI 中文总结
研究有界区域上一类非局部椭圆方程，通过特定方法在适当假设下，证明对于合适区间内的\(\lambda\)，该方程至少有三个弱解。
AI 中文摘要
本文在有界区域\(\Omega\subset {\bf R}^n\)上，考虑形如\(\cases{-\Delta u=Q(u,\lambda)f(u) & 在\(\Omega\)中 \cr & \cr u=0 & 在\(\partial\Omega\)上\cr}\)的非局部问题，在适当假设下，证明了对于\(\lambda\)在合适区间内取值时，每个\(\lambda\)至少存在三个弱解。
英文摘要
In this paper, on a bounded domain $Ω\subset {\bf R}^n$, we consider a nonlocal problem of the type $$\cases{-Δu=Q(u,λ)f(u) & in $Ω$ \cr & \cr u=0 & on $\partialΩ$\cr}$$ where $Q:H^1_0(Ω)\times {\bf R}\to {\bf R}$, proving, under suitable assumptions, the existence of at least three weak solutions for each $λ$ running in a suitable interval.
