论文标题
Lin-Ni-Takagi方程的单数径向溶液
Singular radial solutions for the Lin-Ni-Takagi equation
论文作者
论文摘要
我们研究了lin-ni-takagi方程的奇异辐射对称解决方案，用于尺寸$ n \ geq 3 $中的超临界功率非线性。结果表明，对于任何球和任何$ k \ geq 0 $，都有一个奇异的解决方案，可满足诺伊曼边界条件，并在恒定平衡周围至少振荡$ k $ times。此外，我们表明，如果指数分别大或小于约瑟夫 - 伦格伦指数，则单数解的摩尔斯索引是有限或无限的。
We study singular radially symmetric solution to the Lin-Ni-Takagi equation for a supercritical power non-linearity in dimension $N\geq 3$. It is shown that for any ball and any $k \geq 0$, there is a singular solution that satisfies Neumann boundary condition and oscillates at least $k$ times around the constant equilibrium. Moreover, we show that the Morse index of the singular solution is finite or infinite if the exponent is respectively larger or smaller than the Joseph--Lundgren exponent.
