论文标题
一类半线性椭圆方程的存在和多重性结果
Existence and multiplicity results for a class of semilinear elliptic equations
论文作者
论文摘要
我们研究了非负解的存在和多样性，以及相应参数依赖性分支的行为，对等式$-ΔU=（1-u）u^m-λu^n $在有限的域$ω\ subset \ subset \ subbb {r}^n $ end od dirichlet dirichlet dirichlet dirichlet diricheled diricheled $ 0 $ 0 $ 0 <m n $ 0 <m n $ n $ n $ n $ n $ n $ n $ 0 <m n $ 0 <m n $ n $ 0 <m。当$λ> 0 $时，可以将获得的溶液视为相应的反应扩散方程的稳态，描述了用终止的等温自催化化学反应模型。除了主要的新结果外，我们还制定了一些相关的猜想。
We study the existence and multiplicity of nonnegative solutions, as well as the behaviour of corresponding parameter-dependent branches, to the equation $-Δu = (1-u) u^m - λu^n$ in a bounded domain $Ω\subset \mathbb{R}^N$ endowed with the zero Dirichlet boundary data, where $0<m \leq 1$ and $n>0$. When $λ> 0$, the obtained solutions can be seen as steady states of the corresponding reaction-diffusion equation describing a model of isothermal autocatalytic chemical reaction with termination. In addition to the main new results, we formulate a few relevant conjectures.
