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

Brunovsky, Pavol; Chow, Shui-Nee

J. Differ. Equations 53, 1-23 (1984).

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

Keywords:

Dirichlet boundary condition; stationary solutions; Neumann boundary conditions; time map; Morse function

Citations:

Zbl 0488.58015

References:

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