Abstract:We prove existence and bifurcation results for a semilinear eigenvalue problem in $\Bbb R^N$ $(N\geq 2)$, where the linearization --- $\vartriangle $ has no eigenvalues. In particular, we show that under rather weak assumptions on the coefficients $\lambda =0$ is a bifurcation point for this problem in $H^1, H^2$ and $L^p$ $(2\leq p\leq \infty )$.
Keywords: bifurcation point, variational method, eigenvalues, exponential decay, standing waves
AMS Subject Classification: 35P30, 35A30