关于某些具有竞争系数的标量场方程
On Some Scalar Field Equations with Competing Coefficients
摘要：
本文研究\[ \left\{ \begin{array}{ll} -Δu+α(x)u= β(x)|u|^{p-1}u \quad \hbox{in }\mathbb{R}^N, u(x)>0\quad\hbox{in } \mathbb{R}^N, \qquad u \in H^1(\mathbb{R}^N), \end{array} \right. \]型半线性椭圆问题，其中$p$是超线性但亚临界的，系数$α$和$β$都是正函数，使得$α(x) \to a_\infty > 0$和$β(x)\to b_\infty > 0$为$|x| \to \infty$ .这项工作的目的是描述一些现象时，可能会发生的系数是“竞争”。
英文摘要：
This paper deals with semilinear elliptic problems of the type \[ \left\{ \begin{array}{ll} -Δu+α(x)u= β(x)|u|^{p-1}u \quad \hbox{in }\mathbb{R}^N, u(x)>0\quad\hbox{in } \mathbb{R}^N, \qquad u \in H^1(\mathbb{R}^N), \end{array} \right. \] where $p$ is superlinear but subcritical and the coefficients $α$ and $β$ are positive functions such that $α(x) \to a_\infty > 0$ and $β(x)\to b_\infty > 0$, as $|x| \to \infty$. Aim of this work is to describe some phenomena that can occur when the coefficients are "competing".
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
