2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212990We study the existence and uniqueness of new classes of solutions of the superlinear equation $-Δu+u^q=0$ (q>1) in a domain of R^N or in a finely open set for the topology associated to the Bessel capacity C_{2,q'}. Condition of existence or uniqueness of solutions with boundary blow-up are obtained generalizing the results of Dhersin-Le Gall and of Labutin.A paraître au Journal de Mathématiques Pures et AppliquéesAnalysis of PDEs35J60;35J65;31B15;31C25text