Uniqueness of non-negative solutions of a class of semi-linear elliptic equations
Uniqueness of non-negative solutions of a class of semi-linear elliptic equations
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DOI：
10.1007/978-1-4613-9608-6_1
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
H. Kaper;M. Kwong
中科院分区：
文献类型：
--
作者：
H. Kaper;M. Kwong
研究一类（边值问题）u″ + g（r）u′ + f（u）= 0，r> 0;u′（0）= 0，limr → ∞u（r）= 0;其中f（0）= 0.这样的问题出现在半线性椭圆型微分方程的研究中。在适当的条件下，证明了（BVP）至多有一个非负非平凡解。这些条件比Peletier和Serrin [6]给出的条件弱，他们考虑了特殊情况eg（r）=（n- 1）/r，n= 2，3，n = 1。
This article is concerned with boundary value problems of the type (BVP)u″ + g(r)u′ + f(u) = 0,r> 0;u′(0) = 0, limr → ∞u(r) = 0; wheref(0) = 0. Such problems arise in the study of semi-linear elliptic differential equations in ℝn. It is shown that (BVP) has at most one non-negative non-trivial solution under appropriate conditions onfandg. The conditions are weaker than those given by Peletier and Serrin [6], who considered the special caseg(r) = (n- 1)/r,n= 2, 3,⋯.