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On the evolutionary bifurcation curves for the one-dimensional prescribed mean curvature equation with logistic type
被引:2
|作者:
Zhang, Jiajia
[1
]
Qiao, Yuanhua
[1
]
Duan, Lijuan
[2
]
Miao, Jun
[3
]
机构:
[1] Beijing Univ Technol, Fac Sci, Beijing 100124, Peoples R China
[2] Beijing Univ Technol, Fac Informat Technol, Beijing 100124, Peoples R China
[3] Beijing Informat Sci & Technol Univ, Sch Comp Sci, Beijing 100101, Peoples R China
来源:
OPEN MATHEMATICS
|
2021年
/
19卷
/
01期
基金:
中国国家自然科学基金;
关键词:
mean curvature;
bifurcation curve;
logistic function;
EXACT MULTIPLICITY;
POSITIVE SOLUTIONS;
EXACT NUMBER;
TIME MAPS;
CLASSIFICATION;
NONLINEARITY;
EXISTENCE;
DIAGRAMS;
D O I:
10.1515/math-2021-0070
中图分类号:
O1 [数学];
学科分类号:
0701 ;
070101 ;
摘要:
We study the bifurcation diagrams and exact multiplicity of positive solutions for the one-dimensional prescribed mean curvature equation {-(u'/root 1 + u'(2))' = lambda(u/1 + u)(p), -L < x < L, u(-L) = u(L) = 0, where. is a bifurcation parameter, and L, p > 0 are two evolution parameters. We prove that on the (lambda, parallel to u parallel to(infinity))-plane, for 0 < p <= root 2/4, the bifurcation curve is superset of-shaped bifurcation starting from (0, 0). And for p = 1, f(u) = u/1+u is a logistic function, then the bifurcation curve is also superset of-shaped bifurcation starting from (pi(2)/4L(2), 0). While for p > 1, the bifurcation curve is reversed e-like shaped bifurcation if L > L*, and isexactly decreasing for lambda > lambda* if 0 < L < L-*.
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页码:927 / 939
页数:13
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