Multiple existence of positive even solutions for a two point boundary value problem on some very narrow possible parameter set
Multiple existence of positive even solutions for a two point boundary value problem on some very narrow possible parameter set
复制标题
某些非常窄的可能参数集上两点边值问题的正偶解的多重存在性
DOI：
10.1016/j.jmaa.2022.126182
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Kohtaro Watanabe
中科院分区：
文献类型：
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作者：
Naoki Shioji;Satoshi Tanaka;Kohtaro Watanabe
证明了方程{u ″（x）+（|X| l+ λ）u（x）p= 0，x∈（− 1，1），u（− 1）= u（1）= 0，其中参数l和λ满足l≥ 0和λ≥ 0，指数p满足p> 1.结果表明，当p> 1时，在（l，λ）<$R2的第一象限的大部分区域上，上述问题的正偶解的唯一性成立，且存在多个正偶解的可能区域为一个很窄的集合.因此，期望正偶解的唯一性在（l，λ）<$R 2的第一象限的整个集合上成立似乎是很自然的。与此相反，我们发现在这样一个狭窄的集合中存在一些三元组（l，λ，p），使得正偶数解存在乘数值验证方法的帮助。
The existence of multiple positive even solutions to {u ″(x)+(| x| l+ λ) u (x) p= 0, x∈(− 1, 1), u (− 1)= u (1)= 0, is proved, where the parameters l and λ satisfy l≥ 0 and λ≥ 0 and the exponent p satisfies p> 1. It is shown that for fixed p> 1, on the majority part of the first quadrant of (l, λ)⊂ R 2, the uniqueness of positive even solutions of the above problem holds and a very narrow set remains as the possible region of the existence of multiple positive even solutions. Thus, it seems natural to expect the uniqueness of positive even solutions holds on the whole set of the first quadrant of (l, λ)⊂ R 2. Contrary to this expectation, we find some triples (l, λ, p) in such a narrow set such that positive even solutions exist multiply with the aid of the numerical verification method.