Semilinear elliptic equations of the form ?ni,j=1(aij(cursive Greek chi)ucursive Greek chii(cursive Greek chi))cursive Greek chij + f(?, cursive Greek chi, u(cursive Greek chi)) = 0, cursive ? O, u(cursive Greek chi) - 0, cursive Greek chi ? ?O, are considered, where ? ? R is a parameter, O ? Rn is a bounded domain and f is a smooth non-linear function. It is shown that for 'generic' functions f, the set of non-trivial solutions (?, u) consists of a finite, or countable, collection of smooth, 1-dimensional curves and any such solution is either hyperbolic or is a saddle-node bifurcation point of the curve.
|Number of pages||10|
|Journal||Zeitschrift fur Angewandte Mathematik und Physik|
|Publication status||Published - Sep 1996|
- Reaction-diffusion equations
- Saddle-node bifurcation
- Stationary solutions