论文标题
半椭圆系统的非负整个解决方案的不存在
Nonexistence of nonnegative entire solutions of semilinear elliptic systems
论文作者
论文摘要
我们考虑二阶半线性椭圆系统 $ΔU= p \ left（x \ right）v^α，$ $ΔV= q \ left（x \ right）u^β，$，其中 $ x \ in \ mathbf {r}^n，$ $ n \ geq 3，$ $ $ a $和$β$是正常数， $ P $和$ Q $是非负连续功能。我们证明了非平凡的非负整个解决方案 如果功能$ p $和$ q $是缓慢的衰减，则无法存在。
We consider the second order semilinear elliptic system $Δu= p\left( x\right) v^α,$ $Δv= q\left(x\right) u^β,$ where $x \in \mathbf{R}^N,$ $N \geq 3,$ $α$ and $β$ are positive constants, $p$ and $q$ are nonnegative continuous functions. We prove that nontrivial nonnegative entire solutions fail to exist if the functions $p$ and $q$ are of slow decay.
