The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen

Full-Text PDF (308 KB) | Metadata | Table of Contents | ZAA summary
Volume 33, Issue 2, 2014, pp. 199–215
DOI: 10.4171/ZAA/1507

Published online: 2014-04-25

On a Singular Class of Hamiltonian Systems in Dimension Two

Abbes Benaissa[1] and Brahim Khaldi[2]

(1) Djillali Liabes University, Sidi Bel Abbes, Algeria
(2) University of Bechar, Algeria

Let $\Omega$ be a bounded domain in $\mathbb{R}^{2}$. In this paper, we consider the following systems of semilinear elliptic equations \[ \text{(S)}\left\{ \begin{alignedat}{2} -\Delta u&=\tfrac{g(v)}{|x|^{a}}&\quad &\hbox{ in }\Omega \\ -\Delta v&=\tfrac{f(u)}{|x|^{b}}&& \hbox{ in }\Omega\\ u&=v=0&& \hbox{ on }\partial\Omega , \end{alignedat} \right. \] where $a,b\in[0, 2)$ and the functions $f$ and $g$ are nonlinearities having an exponential growth on $\Omega$. This nonlinearity is motivated by suitable Trudinger-Moser inequality with a singular weight. In fact, we prove the existence of a nontrivial solution to (S). For the proof we use a variational argument (a linking theorem).

Keywords: Variational method, Trudinger-Moser inequality, Hamiltonian systems

Benaissa Abbes, Khaldi Brahim: On a Singular Class of Hamiltonian Systems in Dimension Two. Z. Anal. Anwend. 33 (2014), 199-215. doi: 10.4171/ZAA/1507