Co-bifurcating Branches of solutions for nonlinear eigenvalue problems in Banach spaces

1983 ◽  
Vol 135 (1) ◽  
pp. 119-131 ◽  
Author(s):  
Massimo Furi ◽  
M. Patrizia Pera
Keyword(s):  
Banach Spaces ◽  
Eigenvalue Problems ◽  
Nonlinear Eigenvalue Problems ◽  
Nonlinear Eigenvalue

scholarly journals SOLUTION BRANCHES OF NONLINEAR EIGENVALUE PROBLEMS ON RESTRICTED DOMAINS

2020 ◽  
Vol 102 (3) ◽  
pp. 490-497
Author(s):  
SHANE ARORA
Keyword(s):  
Banach Spaces ◽  
Bifurcation Point ◽  
Eigenvalue Problems ◽  
Accumulation Point ◽  
Nonlinear Eigenvalue Problems ◽  
Restricted Domains ◽  
Nonlinear Eigenvalue

We extend bifurcation results of nonlinear eigenvalue problems from real Banach spaces to any neighbourhood of a given point. For points of odd multiplicity on these restricted domains, we establish that the component of solutions through the bifurcation point either is unbounded, admits an accumulation point on the boundary, or contains an even number of odd-multiplicity points. In the simple-multiplicity case, we show that branches of solutions in the directions of corresponding eigenvectors satisfy similar conditions on such restricted domains.

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