EXISTENCE AND UNIQUENESS OF SINGULAR SOLUTION TO STATIONARY SCHROEDINGER EQUATION WITH SUPERCRITICAL NONLINEARITY

摘要

In this paper, we study a singular solution to the following elliptic equations: {-Δu+|x|~2u-λu-|u|~(P-1)u = 0, x∈R~d, u(x) > 0, x ∈ R~d, u(x)→ 0 as |x|→ ∞, where d ≥ 3, λ > 0 and p > 1. In the spirit of Merle and Peletier [9], we shall show that in case of p > (d + 2)/(d - 2), there is a unique value λ = λ_* such that the equation with λ = λ_* has a unique radial singular solution.