标题： 半正定$φ$-拉普拉斯问题中不存在正径向解的超线性反应项 显示英文标题

标题： Nonexistence of positive radial solutions for semipositone $φ$-Laplacian problems with superlinear reaction term

摘要： 本文的目的是证明在$|x|=1$上，对于足够大的$\lambda>0$，问题$-\Delta_\phi u=\lambda f(u)$，$x\in B_1(0)$，$u(x)=0$的正径向解不存在。 这里，$\phi$是一个连续函数，$\Delta_\phi$表示$\phi$-拉普拉斯算子，其由$\Delta_\phi (u):=div (\phi (|\nabla u|) \nabla u)$定义，而$B_1(0)$是$\mathbb{R}^N$中的单位球，其中$N>1$。 此外，$f$是一个连续的非减函数，满足$f(0)<0$，并且其在无穷处的行为与$\phi$密切相关。 我们的发现以综合形式呈现，同时采用了间接论证和能量分析。 显示英文摘要

摘要： The aim of this paper is to prove the nonexistence of positive radial solutions to the problem $-\Delta_\phi u=\lambda f(u)$, $x\in B_1(0)$, $u(x)=0$ on $|x|=1$, for $\lambda>0$ sufficiently large. Here, $\phi$ is a continuous function, $\Delta_\phi$ denotes the $\phi$-Laplacian operator which is defined by $\Delta_\phi (u):=div (\phi (|\nabla u|) \nabla u)$, and $B_1(0)$ is the unit ball in $\mathbb{R}^N$, with $N>1$. Furthermore, $f$ is a continuous, nondecreasing function such that $f(0)<0$, and its behavior at infinity is intimately related to $\phi$. Our findings are presented in a combined format, employing both an indirect argument and an energy analysis.