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

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of the Mathematical Society of Japan Pub Date : 2021-12-03 DOI:10.2969/jmsj/86168616

R. Kajikiya

引用次数: 3

Abstract

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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Moore–Nehari微分方程的对称和非对称节点解

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the Mathematical Society of Japan 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Mathematical Society of Japan (JMSJ) was founded in 1948 and is published quarterly by the Mathematical Society of Japan (MSJ). It covers a wide range of pure mathematics. To maintain high standards, research articles in the journal are selected by the editorial board with the aid of distinguished international referees. Electronic access to the articles is offered through Project Euclid and J-STAGE. We provide free access to back issues three years after publication (available also at Online Index).