Opis

• Tytuł:
  Concentration of ground state solutions for fractional Hamiltonian systems
• Twórca:
  Torres, César;
  Zhang, Ziheng
• Opis:
  We are concerned with the existence of ground states solutions to the following fractional Hamiltonian systems: $$ \begin{cases} - _tD^{\alpha}_{\infty}(_{-\infty}D^{\alpha}_{t}u(t))-\lambda L(t)u(t)+\nabla W(t,u(t))=0,\\ u\in H^{\alpha}(\mathbb{R},\mathbb{R}^n), \end{cases} \leqno(\mbox{FHS})_\lambda $$ where $\alpha\in (1/2,1)$, $t\in \mathbb{R}$, $u\in \mathbb{R}^n$, $\lambda> 0$ is a parameter, $L\in C(\mathbb{R},\mathbb{R}^{n^2})$ is a symmetric matrix for all $t\in \mathbb{R}$, $W\in C^1(\mathbb{R} \times \mathbb{R}^n,\mathbb{R})$ and $\nabla W(t,u)$ is the gradient of $W(t,u)$ at $u$. Assuming that $L(t)$ is a positive semi-definite symmetric matrix for all $t\in \mathbb{R}$, that is, $L(t)\equiv 0$ is allowed to occur in some finite interval $T$ of $\mathbb{R}$, $W(t,u)$ satisfies the Ambrosetti-Rabinowitz condition and some other reasonable hypotheses, we show that (FHS)$_\lambda$ has a ground sate solution which vanishes on $\mathbb{R}\setminus T$ as $\lambda \to \infty$, and converges to $u\in H^{\alpha}(\mathbb{R}, \mathbb{R}^n)$, where $u\in E_{0}^{\alpha}$ is a ground state solution of the Dirichlet BVP for fractional systems on the finite interval $T$. Recent results are generalized and significantly improved.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Data:
  2017.10.01
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 50, No 2 (December 2017); 623 - 642;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.033/13093 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.033/13094
• Temat i słowa kluczowe:
  Fractional Hamiltonian systems;
  fractional Sobolev space;
  ground state solution;
  critical point theory;
  concentration phenomena;
  Primary;
  34C37;
  Secondary;
  35A15;
  35B38
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.033
• Dostawca danych:
  Akademicka Platforma Czasopism
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