The boundary blow-up rate of large solutions
The boundary blow-up rate of large solutions
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DOI：
10.1016/j.jde.2003.06.003
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发表时间：
2003-11
影响因子：
2.4
通讯作者：
J. López-Gómez
中科院分区：
文献类型：
--
作者：
J. López-Gómez
本文确定了一类次线性椭圆型边值问题的大解的爆破速率，该问题的非线性项在边界上消失，且非线性项在边界上消失的速率随边界点x∞∈ Ω不同而不同.以前文献中的所有结果都假设了潜在权函数的衰减率在<$Ω的任何一点上都是相同的。这一假设大大简化了问题的数学分析，因为它允许在一个开邻域中构造全局子解和上解。获得一般结果需要在边界的每个特定点进行局部化，这使得特别涉及问题的数学分析。
In this paper we ascertain the blow-up rate of the large solutions of a class of sublinear elliptic boundary value problems with a weight function in front of the nonlinearity that vanishes on the boundary of the underlying domain, Ω , at different rates according to the point of the boundary, x∞∈∂Ω . All previous results in the literature assumed the decay rate of the underlying weight function to be the same at any point of ∂Ω . This hypothesis substantially simplified the mathematical analysis of the problem, as it allowed constructing global sub and supersolutions in an open neighborhood of ∂Ω . Obtaining general results requires localizing at each particular point of the boundary, making particularly involved the mathematical analysis of the problem.