Lin-Ni-Takagi方程的奇异径向解
Singular radial solutions for the Lin-Ni-Takagi equation
摘要：
研究了$N\geq 3$维超临界幂次非线性Lin-Ni-Takagi方程的奇异径向对称解.结果表明，对于任何球和任何$k \geq 0$，都存在一个满足Neumann边界条件的奇异解，并且绕常数平衡振荡至少$k$次。进一步证明了当Morse指数大于或小于Joseph-Lundgren指数时，奇异解的Morse指数是有限的或无限的.
英文摘要：
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.
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