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arXiv · 2106.15431

Non-degeneracy and existence of new solutions for the Schr\"odinger equations

Yuxia Guo·Monica Musso·Shuangjie Peng·Shusen Yan
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Abstract

We consider the following nonlinear problem $$ (P) \quad \quad - \Delta u + V(|y|)u=u^{p},\quad u>0 \quad \mbox{in} \ {\mathbb{R}}^N, \quad u \in H^1({\mathbb{R}}^N), $$ where $V(r)$ is a positive function, $1<p <\frac{N+2}{N-2}$. We show that the multi-bump solutions constructed in [20] is non-degenerate in a suitable symmetric space. We also use this non-degenerate result to construct new solutions for (P).

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Yuxia Guo, Monica Musso, Shuangjie Peng, Shusen Yan. 2021-06-29. Non-degeneracy and existence of new solutions for the Schr\"odinger equations. https://arxiv.org/abs/2106.15431

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