scholarly journals Global branch from the second eigenvalue for a semilinear Neumann problem in a ball

2010 ◽  
Vol 249 (8) ◽  
pp. 1853-1870 ◽  
Author(s):  
Yasuhito Miyamoto
Keyword(s):  
Neumann Problem ◽  
Second Eigenvalue ◽  
Global Branch

scholarly journals A global branch of solutions to a semilinear equation on an unbounded interval

1985 ◽  
Vol 101 (3-4) ◽  
pp. 273-282 ◽  
Author(s):  
C. A. Stuart
Keyword(s):  
Differential Equation ◽  
Neumann Problem ◽  
Order Differential Equation ◽  
Second Order ◽  
Semilinear Equation ◽  
Second Order Differential Equation ◽  
Unbounded Interval ◽  
The Neumann Problem ◽  
Global Branch

SynopsisFor a semilinear second order differential equation on (0, ∞), conditions are given for the bifurcation and asymptotic bifurcation in Lp of solutions to the Neumann problem. Bifurcation occurs at the lowest point of the spectrum of the linearised problem. Under stronger hypotheses, there is a global branch of solutions. These results imply similar conclusions for the same equation on R with appropriate symmetry.

Neumann problem

1993 ◽  
Vol 70 (2) ◽  
pp. 247-281 ◽  
Author(s):  
Wei-Ming Ni ◽  
Izumi Takagi
Keyword(s):  
Neumann Problem
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