论文标题
在超细胞方程式上
On a hyper-singular equation
论文作者
论文摘要
考虑方程$ v = v_0+\ int_0^t（t-s）^{λ-1} v（s）ds $，$λ\ neq 0，-1，-2 ... $和$ v_0 $是一种流畅的函数，与所有衍生物一起迅速衰减。事实证明，该方程的解决方案确实存在，是唯一的，比单数函数$ t^{ - \ frac 5 4} $更光滑。
The equation $v=v_0+\int_0^t(t-s)^{λ-1}v(s)ds$ is considered, $λ\neq 0,-1,-2...$ and $v_0$ is a smooth function rapidly decaying with all its derivatives. It is proved that the solution to this equation does exist, is unique and is smoother than the singular function $t^{-\frac 5 4}$.
