Abstract
We prove a new result on bifurcating branches of bound states for the nonlinear radially symmetric Schrödinger equation $$ -\Delta u =w(|x|)|u|^{\sigma}u -\lambda^2u \ \ \text{ on ${\mathbb{R}}^N$.} $$ We show that, under suitable assumptions on $w$ and $\sigma$, there exist infinitely many continua of nontrivial bound states $u_\lambda$ which emanate from the trivial solution branch at $\lambda=0$. These continua reach arbitrarily large values of $\lambda$, and they are distinguished by the number of nodal domains of the corresponding solutions $u_\lambda$.
Citation
Tobias Weth. "Global bifurcation branches for radially symmetric Schrödinger equations." Adv. Differential Equations 10 (7) 721 - 746, 2005. https://doi.org/10.57262/ade/1355867829
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