# Article

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Keywords:
bifurcation point; variational method; eigenvalues; exponential decay; standing waves
Summary:
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 $L^p$ $(2\leq p\leq \infty )$.
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