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

Stuart, C. A.

Proc. Lond. Math. Soc., III. Ser. 57, No. 3, 511-541 (1988).

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

Keywords:

\(L^ p\)-bifurcation; constrained; minimization; Sobolev spaces; nonlinear eigenvalue problem; semilinear; spectrum; linearisation; variational structure

Citations:

Zbl 0527.35010