Monotone iterative sequences for non-local elliptic problems
Monotone iterative sequences for non-local elliptic problems
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DOI：
10.1017/s0956792511000246
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发表时间：
2011-07
影响因子：
1.9
通讯作者：
M. Al-Refai;N. Kavallaris;M. Hajji
中科院分区：
文献类型：
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作者：
M. Al-Refai;N. Kavallaris;M. Hajji
本文建立了一类具有Dirichlet边界条件的非局部椭圆型微分方程解的存在唯一性结果，该结果一般不接受极大值原理。我们引入了一个单调的上下解对序列，并证明了该序列一致收敛于问题的实际解，这是对一定范围的λ(问题的参数)唯一的解。通过收敛阶大于1的算例验证了迭代序列的收敛。
In this paper we establish an existence and uniqueness result for a class of non-local elliptic differential equations with the Dirichlet boundary conditions, which, in general, do not accept a maximum principle. We introduce one monotone sequence of lower–upper pairs of solutions and prove uniform convergence of that sequence to the actual solution of the problem, which is the unique solution for some range of λ (the parameter of the problem). The convergence of the iterative sequence is tested through examples with an order of convergence greater than 1.