Abstract
We present a survey of works from the last two decades, on positive solutions of the equation ‐Δμ+μq = 0, q>1, in a smooth bounded domain in RN. The central problem is the characterization of positive solutions in terms of their behavior at the boundary. For 1<q≤2 the problem is strongly related to branching processes and superdiffusions. The research progressed, in parallel, through the probabilistic approach on the one hand and the analytic approach on the other hand.
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