Generic properties of stationary state solutions of reaction-diffusion equations.(English)Zbl 0544.34019

The authors consider stationary solutions of the equation $$u''+f(u)=0,$$ with homogeneous Dirichlet or Neumann boundary conditions. They prove that the ”time map” $$\eta \to T(\eta)$$ is generically a Morse function. A simpler proof was also given by the reviewer and A. Wasserman [ibid. 52, 432-438 (1984; Zbl 0488.58015)].
Reviewer: J.Smoller

MSC:

 34B99 Boundary value problems for ordinary differential equations 37D15 Morse-Smale systems

Zbl 0488.58015
Full Text:

References:

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