Resumen de Bubble tower solutions for supercritical elliptic problem in R^N

Wenjing Chen, Juan Dávila, Ignacio Guerra

• We consider the problem ( −1u + u = u p + "uq u > 0 in RN u(z) !0 as |z| !1 where p = p⇤ + ", with p⇤ = N+2 N−2 , while 1 < q < N+2 N−2 if N % 4, and 3 < q < 5 if N = 3, " > 0, and " is a positive parameter. We prove that for " > 0 small enough, the problem has a solution with the shape of a tower of bubbles.