## Bifurcation in $$L^ p({\mathbb{R}}^ N)$$ for a semilinear elliptic equation.(English)Zbl 0673.35005

The author considers a nonlinear eigenvalue problem for a semilinear elliptic operator. The spectrum of the linearisation about the trivial solution is the interval $$[0,\infty)$$. The method used is based on the variational structure of the problem. Unlike his previous papers on a similar topic, the author drops out the radial symmetry assumption, used for example by the author [Lect. Notes Math. 1017, 575-596 (1983; Zbl 0527.35010)].
Reviewer: M.Tucsnak

### MSC:

 35B32 Bifurcations in context of PDEs 35J60 Nonlinear elliptic equations 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs

Zbl 0527.35010
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