Classical and Weak Solutions of a Singular Semilinear Elliptic Problem
Classical and Weak Solutions of a Singular Semilinear Elliptic Problem
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DOI：
10.1006/jmaa.1997.5470
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发表时间：
1997-07
影响因子：
1.3
通讯作者：
A. V. Lair;A. W. Shaker
中科院分区：
文献类型：
--
作者：
A. V. Lair;A. W. Shaker
本文证明了奇异半线性椭圆方程Δu + p（x）f（u）= 0在Rn中存在唯一的正古典解，当p（x）是一个非平凡非负连续函数且满足∞0 t max时，该解在∞处衰减到零|X| = tp（x）dt < ∞，条件是f是（0，∞）上的非增连续可微函数。证明了当p（x）∈ L2且f（s）ds < ∞时，该方程在有界区域上存在唯一的弱H10-解.
The singular semilinear elliptic equation Δu + p(x)f(u) = 0 is shown to have a unique positive classical solution inRnthat decays to zero at ∞ ifp(x) is simply a nontrivial nonnegative continuous function satisfying ∫∞0 t max|x| = t p(x) dt < ∞, providedfis a non-increasing continuously differentiable function on (0, ∞). It is also shown that the equation has a unique weakH10-solution on a bounded domain provided ∫e0 f(s) ds < ∞ andp(x) ∈ L2.