Bifurcation from the Continuous Spectrum in Lp(ℝ)
Charles A. Stuart · Birkhäuser Basel eBooks · 1987
The study of small solutions of the nonlinear eigenvalue problem: $$ \Delta {\text{u(x)}}\, + \,\lambda {\text{u(x)}}\, + \,{\text{q(x)}}\,\left| {\text{u(x)}} \right|^\sigma {\text{u(x)}}\, = \,0 {\text { for x}}\, \in \,{\text{IR}}^{\text{N}} $$ $$ \eqalign{ & \lim \,{\text{u(x)}}\, = \,0 \cr & \left| {\text{x}} \right| \to \infty \cr} $$ where σ > 0 and q: ℝN → ℝ are given, leads to questions involving bifurcation from the continuous spectrum since its linearisation about u ≡ 0 has the interval [0,∞) as spectrum.