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Existence of Bifurcation for An Operator Equation with Zero Derivative(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
1997年02期
Page:
85-88
Research Field:
Publishing date:

Info

Title:
Existence of Bifurcation for An Operator Equation with Zero Derivative
Author(s):
Shuai Jiaqi Hong\ Youcheng
School of Sciences, NUST, Nanjing 210094
Keywords:
bifurcat ion homotopy degree of mapping compact operators
PACS:
O241
DOI:
-
Abstract:
T his paper proves the exist ence of bifurcat ion f or an operat or equat ion mμA x + N ( μ, x ) = 0 with zero derivative near ( μ, x ) = ( 0, 0) by method of homot opy and degree of mapping, w here x ∈X , L∈( 0, μ0) . X and Y are Banach spaces. A : X →Y is bounded linear Fredholm operat or with zero index. N: X →Y is complet ely cont inuous nonlinear operator for f ixed L ∈( 0, μ0 ) , sat isfying N ( μ, 0) = 0 for L∈R. N ( μ, x ) = o( úx ú) ( úx ú→0) . úN ( μ, x ) ú/ úx ú→+ ∞ ( úx ú→+ ∞) . úN( μ, x) ú≥LAúx ú1+ D f or r > 0 suff iciently small and úx ú≥r, A< 1, D> 0, L∈( 0, μ0) ) . ker A is n dimensional space. Under above condit ions, proves the ex is tence of nont rivial solut ion x (μ) near ( 0, 0) and x (μ) →0( μ→0+ ) .

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Memo:
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Last Update: 2013-03-29