Non-degeneracy of double-tower solutions for nonlinear Schrödinger equation and applications

Abstract

This paper is concerned with the following nonlinear Schrödinger equation \begin{equation} \label{eq} - Δu + V(|y|)u=u^{p},\quad u>0 \ \ \mbox{in} \ \mathbb {R}^N, \ \ \ u \in H^1(\mathbb {R}^N), \end{equation} where $V(|y|)$ is a positive function, $1<p<\frac{N+2}{N-2}$. Based on the local Pohozaev identities and blow-up analysis, we first prove a non-degeneracy result for double-tower solutions constructed in [18] in a suitable symmetric space. As an application, we obtain the existence of new type solutions for (0.1).

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