Geometry of phase space and solutions of semilinear elliptic equations in a ball
Geometry of phase space and solutions of semilinear elliptic equations in a ball
复制标题
相空间的几何和球中半线性椭圆方程的解
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
I. Flores
中科院分区：
文献类型：
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作者：
J. Dolbeault;I. Flores
考虑问题{-Δu= up +λu in in B，u>0 in B，u=0 on n B，其中B表示RN中的单位球，N > 3，A > 0且p > 1. Merle和Peletier证明了当p > N+2/N-2时，存在唯一值A = λ* > 0，使得存在径向奇异解.这个值是唯一的一个无界序列的经典解决方案（1）可以积累。这里我们证明了：如果在B中附加p 0 0，则u = 0，其中f（s）= sp + sq，1
We consider the problem {-Δu=u p +λu in in B, u>0 in B, u=0 on ∂B, where B denotes the unit ball in R N , N > 3, A > 0 and p > 1. Merle and Peletier showed that for p > N+2/N-2 there is a unique value A = λ* > 0 such that a radial singular solution exists. This value is the only one at which an unbounded sequence of classical solutions of (1) may accumulate. Here we prove that if additionally p 0 0 in B, u = 0 on ∂B, where f(s) = s p + s q , 1 < q < p, and p satisfies the same condition as above.