2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162451For the equation (-Δu = | |x|-2 |^αu^{p-1}), (1 < |x| < 3), we prove the existence of two solutions for (α) large, and of two additional solutions when (p) is close to the critical Sobolev exponent (2^*=2N/(N-2)). A symmetry--breaking phenomenon appears, showing that the least--energy solutions cannot be radial functions.Final version, accepted by Journal of Differential EquationsAnalysis of PDEs35J40text