On a Singular Class of Hamiltonian Systems in Dimension Two

Abbes Benaissa; Brahim Khaldi

doi:10.4171/zaa/1507

JournalszaaVol. 33, No. 2pp. 199–215

On a Singular Class of Hamiltonian Systems in Dimension Two

Abbes Benaissa
Djillali Liabes University, Sidi Bel Abbes, Algeria
Brahim Khaldi
University of Bechar, Algeria

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Abstract

Let $Ω$ be a bounded domain in $R^{2}$ . In this paper, we consider the following systems of semilinear elliptic equations

(S) ⎩ ⎨ ⎧ - Δ u - Δ v u = \frac{g ( v )}{∣ x ∣ ^{a}} = \frac{f ( u )}{∣ x ∣ ^{b}} = v = 0 in Ω in Ω on \partial Ω,

where $a, b \in [0, 2)$ and the functions $f$ and $g$ are nonlinearities having an exponential growth on $Ω$ . 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).

Cite this article

Abbes Benaissa, Brahim Khaldi, On a Singular Class of Hamiltonian Systems in Dimension Two. Z. Anal. Anwend. 33 (2014), no. 2, pp. 199–215

DOI 10.4171/ZAA/1507