科研之友
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摘要
We study positive solutions of the equation Delta u = u(-p) - 1 in Omega C R-N (N >= 2), where p > 0 and Omega is a bounded or unbounded domain. We show that there is a number p(c) = p(c)(N) >= 0 such that this equation with Omega = R-N has no stable positive solution for p > p(c). We further show that there is a critical power p(c) = p(c)(N) such that if p > p(c). this equation with Omega = B-r\{0} has no positive solution with finite Morse index that has an isolated rupture at 0; if 0 < p <= p(c). this equation with Omega = B-r\{0} has a positive solution with finite
