English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This paper is dedicated to studying the following elliptic system ofHamiltonian type: $$\left\{ \begin{array}{ll} -\varepsilon^2\triangleu+u+V(x)v=Q(x)F_{v}(u, v), \ \ \ \ x\in \mathbb{R}^N,\\ -\varepsilon^2\trianglev+v+V(x)u=Q(x)F_{u}(u, v), \ \ \ \ x\in \mathbb{R}^N,\\ |u(x)|+|v(x)|\rightarrow 0, \ \ \mbox{as} \ |x|\rightarrow \infty, \end{array}\right. $$where $N\ge 3$, $V, Q\in \mathcal{C}(\mathbb{R}^N, \mathbb{R})$, $V(x)$ isallowed to be sign-changing and $\inf Q > 0$, and $F\in\mathcal{C}^1(\mathbb{R}^2, \mathbb{R})$ is superquadratic at both $0$ andinfinity but subcritical. Instead of the reduction approach used in [Calc VarPDE, 2014, 51: 725-760], we develop a more direct approach -- non-Neharimanifold approach to obtain stronger conclusions but under weaker assumptionsthan these in [Calc Var PDE, 2014, 51: 725-760]. We can find an$\varepsilon_0>0$ which is determined by terms of $N, V, Q$ and $F$, then weprove the existence of a ground state solution of Nehari-Pankov type to thecoupled system for all $\varepsilon\in (0, \varepsilon_0]$.

Existence of ground state solutions of Nehari-Pankov type to Schr\"odinger systems