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arXiv · 1505.07488

Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schr\"odinger equations

Weiwei Ao·Monica Musso·Juncheng Wei
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Abstract

We prove that the non-radial sign-changing solutions to the nonlinear Schr\"odinger equation \begin{equation*} \Delta u-u+|u|^{p-1}u=0 \mbox{ in }\R^N, \quad u \in H^1 (\R^N ) \end{equation*} constructed by Musso, Pacard and Wei is non-degenerate. This provides the first example of non-degenerate sign-changing solution with finite energy to the above nonlinear Schr\"odinger equation.

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Weiwei Ao, Monica Musso, Juncheng Wei. 2015-05-27. Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schr\"odinger equations. https://arxiv.org/abs/1505.07488

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