论文标题
在半线性椭圆形BVP中生成环和壳
Generating loops and isolas in semilinear elliptic BVP's
论文作者
论文摘要
在本文中，我们确定了一组正面和负面解决方案的全局$λ$ - 从$ u = 0 $分叉的全局$ u = 0 $，对于半连续的椭圆形BVP \ begin {equation*} \ left \ left \ left {\ okent {array {array} u \ rangle+u+λu^{2} -u^{q}＆\ text {in}ω，\\ u = 0＆\ text {on} \partialΩ，\ end end {array} \ right。根据$ d> 0 $的值和整数$ q \ geq 4 $。图1.1-1.3根据$ d $和$ q $的值总结了本文的主要发现。请注意，参数$λ$在此模型中所起的作用非常特别，因为除了测量对流的强度外，它还量化了非线性项$λu^2 $的幅度。我们将这个问题视为一种数学玩具，以生成反应扩散方程中的溶液回路和ISLAS。
In this paper, we ascertain the global $λ$-structure of the set of positive and negative solutions bifurcating from $u=0$ for the semilinear elliptic BVP \begin{equation*} \left\{\begin{array}{ll} -dΔu= λ\langle \mathfrak{a},\nabla u\rangle+u+λu^{2}-u^{q} & \text{ in } Ω, \\ u=0 & \text{ on } \partialΩ, \end{array}\right. \end{equation*} according to the values of $d>0$ and the integer number $q\geq 4$. Figures 1.1-1.3 summarize the main findings of this paper according to the values of $d$ and $q$. Note that the role played by the parameter $λ$ in this model is very special, because, besides measuring the strength of the convection, it quantifies the amplitude of the nonlinear term $λu^2$. We regard to this problem as a mathematical toy to generate solution loops and isolas in Reaction Diffusion equations.
