具有变号位势和吸收项的非线性eigenvalue Logistic问题的整体解
Entire solutions of the nonlinear eigenvalue logistic problem with sign-changing potential and absorbtion
摘要：
研究了在$\RR^N$中Logistic方程$-Δu=λ(V(x)u-f(u))$的正解在无穷远处衰减到零的问题，其中$V(x)$是一个变号的位势，$λ$是一个实参数，$f$是一个吸收项，使得映射$f(t)/t$在$(0,\infty)$中是递增的.证明了存在一个分歧非负数$Λ$使得当$λ>Λ$时上述问题有唯一解，但当$λ\leqΛ$时不存在这样的解.
英文摘要：
We are concerned with positive solutions decaying to zero at infinity for the logistic equation $-Δu=λ(V(x)u-f(u))$ in $\RR^N$, where $V(x)$ is a variable potential that may change sign, $λ$ is a real parameter, and $f$ is an absorbtion term such that the mapping $f(t)/t$ is increasing in $(0,\infty)$. We prove that there exists a bifurcation non-negative number $Λ$ such that the above problem has exactly one solution if $λ>Λ$, but no such a solution exists provided $λ\leqΛ$.
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