The structure of a set of positive solutions to Dirichlet BVPs with time and space singularities
The structure of a set of positive solutions to Dirichlet BVPs with time and space singularities
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DOI：
10.1515/gmj-2013-0002
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发表时间：
2013-01-01
影响因子：
0.7
通讯作者：
Weinmueller, Ewa B.
中科院分区：
文献类型：
--
作者：
Rachunkova, Irena;Spielauer, Alexander;Weinmueller, Ewa B.
讨论了奇异Dirichlet边值问题mu '(t) + a/tu'(t) - a/t(2)u(t) = f(t, u(t), u'(t)), u(0) = 0, u(t) = 0的可解性。这里a是（-∞,-1）的一个元素，f在[0，T] x D上满足局部卡拉多条件，其中D =(0,∞)x r。证明了问题所有正解的集合L的基数是一个连续体。此外，还描述了集合L的结构和性质。给出了结果的应用和数值模拟。
The paper discusses the solvability of the singular Dirichlet boundary value problemu ''(t) + a/tu'(t) - a/t(2)u(t) = f(t, u(t), u'(t)), u(0) = 0, u(T) = 0.Here a is an element of (-infinity, -1) and f satisfies the local Caratheodory conditions on [0, T] x D, where D = (0, infinity) x R. It is shown that the cardinality of the set L of all positive solutions to the problem is a continuum. In addition, the structure and properties of the set L are described. Applications and numerical simulations of the results are presented.