Description

• Title:
  Existence of solutions for singularly perturbed Hamiltonian elliptic systems with nonlocal nonlinearities
• Creator:
  Yang, Minbo;
  Wei, Yuanhong
• Description:
  In the present paper we study singularly perturbed Hamiltonian elliptic systems with nonlocal nonlinearities $$ \cases \displaystyle -\vr^2\Delta u +V(x)u =\bigg(\int_{\mathbb{R}^N} \frac{|z|^{p}}{|x-y|^{\mu}}dy\bigg)|z|^{p-2}u, \\ \displaystyle -\vr^2\Delta v +V(x)v =-\bigg(\int_{\mathbb{R}^N} \frac{|z|^{p}}{|x-y|^{\mu}}dy\bigg)|z|^{p-2}v, \endcases $$ where $z=(u,v)\in H^1(\mathbb{R}^N,\mathbb{R}^2)$, $V(x)$ is a continuous real function on $\mathbb{R}^N$, $0< \mu< N$ and $2-{\mu}/{N}< p< ({2N-\mu})/({N-2})$. Under suitable assumptions on the potential $V(x)$, we can prove the existence of solutions for small parameter $\varepsilon$ by variational methods. Moreover, if $N> 2$ and $2+({2-\mu})/({N-2})< p< ({2N-\mu})/({N-2})$ then the solutions $z_\varepsilon\to 0$ as the parameter $\varepsilon\to 0$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.04.12
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 43, No 2 (June 2014); 385 - 402;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2014.023/8137
• Subject:
  Hamiltonian elliptic systems;
  generalized linking theorem;
  (PS) condition;
  variational methods;
  35J45;
  35J50;
  35J60;
  35A15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2014.023
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other