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arXiv · 1511.02165

Semilinear equations associated with Dunkl Laplacian

Mohamed Ben Chrouda·Khalifa El Mabrouk·Kods Hassine
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Abstract

Let $Δ_k$ be the Dunkl Laplacian on $\mathbb R^d$ associated with a reflection group $W$ and a multiplicity function $k$. The purpose of this paper is to establish necessary and sufficient condition under which there exists a positive solution of the equation $Δ_ku=φ(u)$ in the unit ball of $\mathbb R^d$ as well as in the whole space $\mathbb R^d$.

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Mohamed Ben Chrouda, Khalifa El Mabrouk, Kods Hassine. 2015-11-05. Semilinear equations associated with Dunkl Laplacian. https://arxiv.org/abs/1511.02165

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