On the number of stable positive solutions of weakly nonlinear elliptic equations when the diffusion is small

2021 ◽  
pp. 1
Author(s):  
Edward N. Dancer
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Weakly Nonlinear ◽  
Nonlinear Elliptic

Stable and Finite Morse Index Solutions for Dirichlet Problems with Small Diffusion in a Degenerate Case and Problems with Infinite Boundary Values

2009 ◽  
Vol 9 (4) ◽  
Author(s):  
E.N. Dancer
Keyword(s):  
Elliptic Equations ◽  
Morse Index ◽  
Nonlinear Elliptic Equations ◽  
Degenerate Case ◽  
Boundary Values ◽  
Dirichlet Problems ◽  
Small Diffusion ◽  
Weakly Nonlinear ◽  
Nonlinear Elliptic

AbstractWe consider weakly nonlinear elliptic equations with small diffusion in the case where the nonlinearity has a non-nodal zero. We show that there is an unexpected connection with problems with infinite boundary values.

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