Positive solutions of a logistic equation on unbounded intervals

被引：6
作者：
Ma, L [1 ]
Xu, XW
机构：
[1] Tsing Hua Univ, Dept Math Sci, Beijing 100084, Peoples R China
[2] Natl Univ Singapore, Dept Math, Singapore 119260, Singapore
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2002年 / 130卷 / 10期
关键词：
direct method; blow-up; positive solution;
D O I：
10.1090/S0002-9939-02-06405-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the existence of positive solutions of a one-parameter family of logistic equations on R+ or on R. These equations are stationary versions of the Fisher equations and the KPP equations. We also study the blow-up region of a sequence of the solutions when the parameter approaches a critical value and the non-existence of positive solutions beyond the critical value. We use the direct method and the sub and super solution method.
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收藏
页码：2947 / 2958
页数：12
相关论文
共 21 条
[11]   LINEAR AND SEMILINEAR EIGENVALUE PROBLEMS IN R(N) [J].
EDELSON, AL ;
RUMBOS, AJ .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (1-2) :215-240
[12]   Principal eigenvalues with indefinite weight functions [J].
Jin, ZR .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (05) :1945-1959
[13]  
Kazdan JL., 1975, J. Differential Geometry, V10, P113, DOI 10.4310/jdg/1214432678
[14]   On the elliptic equation Δu+ku-Kup=0 on complete Riemannian manifolds and their geometric applications [J].
Li, P ;
Tam, LF ;
Yang, DG .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 350 (03) :1045-1078
[15]  
Lin F. H., 1985, Proc. Am. Math. Soc., V95, P219
[16]   First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs [J].
Lopez-Gomez, J ;
de Lis, JCS .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 148 (01) :47-64
[17]  
Ma L, 1993, MATH ANN, V295, P75, DOI [10.1007/BF01444877, DOI 10.1007/BF01444877]
[18]   Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations [J].
Marcus, M ;
Veron, L .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (02) :237-274
[19]  
NI WM, 1982, INDIANA U MATH J, V31, P495
[20]   ON THE POSITIVE SOLUTIONS OF SEMILINEAR EQUATIONS DELTA-U+LAMBDA-U-HUP=0 ON THE COMPACT MANIFOLDS [J].
OUYANG, TC .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 331 (02) :503-527
123