The Generalized Saddle-Node Bifurcation of Degenerate Solution

Ping Liu, and Yu-Wen Wang. "The Generalized Saddle-Node Bifurcation of Degenerate Solution." Commentationes Mathematicae 45.2 (2005): null. <http://eudml.org/doc/291703>.

@article{PingLiu2005,
abstract = {In this paper we discuss the bifurcation problem for the abstract operator equation of the form $F (u, \lambda ) = \theta $ with a parameter $\lambda $, where $F\colon X \times R \rightarrow Y$ is a $C^1$ mapping, $X, Y$ are Banach spaces. By the bounded linear generalized inverse $A^+$ of $A = F_u (u_0 , \lambda _0 )$, an abstract bifurcation theorem for the case $\operatorname\{dim\}N (F_u (u_0 , \lambda _0 )) \ge \operatorname\{codim\} R(F_u (u_0 , \lambda _0 )) = 1$ has been obtained.},
author = {Ping Liu, Yu-Wen Wang},
journal = {Commentationes Mathematicae},
keywords = {Operator equation; bifurcation; generalized inverse of operator},
language = {eng},
number = {2},
pages = {null},
title = {The Generalized Saddle-Node Bifurcation of Degenerate Solution},
url = {http://eudml.org/doc/291703},
volume = {45},
year = {2005},
}

TY - JOUR
AU - Ping Liu
AU - Yu-Wen Wang
TI - The Generalized Saddle-Node Bifurcation of Degenerate Solution
JO - Commentationes Mathematicae
PY - 2005
VL - 45
IS - 2
SP - null
AB - In this paper we discuss the bifurcation problem for the abstract operator equation of the form $F (u, \lambda ) = \theta $ with a parameter $\lambda $, where $F\colon X \times R \rightarrow Y$ is a $C^1$ mapping, $X, Y$ are Banach spaces. By the bounded linear generalized inverse $A^+$ of $A = F_u (u_0 , \lambda _0 )$, an abstract bifurcation theorem for the case $\operatorname{dim}N (F_u (u_0 , \lambda _0 )) \ge \operatorname{codim} R(F_u (u_0 , \lambda _0 )) = 1$ has been obtained.
LA - eng
KW - Operator equation; bifurcation; generalized inverse of operator
UR - http://eudml.org/doc/291703
ER -