Symmetric and asymmetric nodal solutions for the Moore–Nehari differential equation
Symmetric and asymmetric nodal solutions for the Moore–Nehari differential equation
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DOI：
10.2969/jmsj/86168616
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发表时间：
2021-12
影响因子：
0.7
通讯作者：
R. Kajikiya
中科院分区：
文献类型：
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作者：
R. Kajikiya
我们考虑Moore-nehari方程u‘’+h(x，λ)|u|p−1u=0 in(−1，1)其中u(−1)=u(1)=0，其中p>；1，h(x，λ)=0对于|x|lt；λ，h(x，λ)=1对于λ≤|x|≤1，λ∈(0，1)是参数。我们证明了对于给定的非负整数m和n，在区间(−1，0)中恰好有m个零点，在(0，1)中恰好有n个零点的解的存在性。
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.