| Abstract: |
| Abstract: We discuss the existence of localized sign-changing solutions for the semiclassical nonlinear Schr\odinger equation with the potential $V$ assumed to be bounded and bounded away from zero. When V has a local minimum point $P$, as $\epsilon \to 0$, we construct an infinite sequence of localized sign-changing solutions clustered at $P$ and these solutions are of higher topological type in the sense that they are obtained from a minimax characterization of higher dimensional symmetric linking structure via the symmetric mountain pass theorem. Our method is rather robust without using any non-degeneracy condition. |
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