Moore–Nehari微分方程的对称和非对称节点解

Pub Date : 2021-12-03 DOI:10.2969/jmsj/86168616

R. Kajikiya

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引用次数: 3

摘要

我们考虑Moore-Nehari方程，u′′′+h（x，λ）|u|p−1u=0在（−1，1）中，u（−1）=u（1）=0，其中p>1，h（x、λ）=0对于|x|<λ，h（x、λ）=1对于λ≤|x|≤1，λ∈（0，1）是一个参数。对于给定的非负整数m和n，我们证明了一个解的存在性，该解在区间（−1，0）中正好有m个零，在区间（0，1）中恰好有n个零。

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Symmetric and asymmetric nodal solutions for the Moore–Nehari differential equation

We consider the Moore-Nehari equation, u′′+h(x, λ)|u|p−1u = 0 in (−1, 1) with u(−1) = u(1) = 0, where p > 1, h(x, λ) = 0 for |x| < λ, h(x, λ) = 1 for λ ≤ |x| ≤ 1 and λ ∈ (0, 1) is a parameter. We prove the existence of a solution which has exactly m zeros in the interval (−1, 0) and exactly n zeros in (0, 1) for given nonnegative integers m and n.

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