关于无穷点bc的Robin问题

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-10 DOI:10.1112/blms.70018

Chiun-Chang Lee

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引用次数: 0

摘要

研究具有robin型无穷点边界条件的半线性方程，其边界条件非局部依赖于无穷多个内点的解。为了克服这些模型中缺乏保证变分结构所带来的困难，我们建立了与边界条件相对应的映射。通过结合渐近分析和不动点论证，证明了在特定假设下解的存在性。这种方法在相关研究中是新颖的。

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On Robin problems with infinite-point BCs

We study semilinear equations with Robin-type infinite-point boundary conditions, where the boundary conditions depend nonlocally on the solution at infinitely many interior points. To overcome the difficulties arising from the lack of guaranteed variational structure in these models, we establish mappings that correspond to the boundary conditions. Through a combination of asymptotic analysis and fixed-point arguments, we prove the existence of solutions under specific assumptions. This approach is novel in related research.

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