Limits as p→∞p→∞ of p-Laplacian problems with a superdiffusive power-type nonlinearity: Positive and sign-changing solutions

We investigate the asymptotic behaviour as p→∞p→∞ of sequences of solutions of the equation{−Δpu=λ|u|q(p)−2uin Ω,u=0on ∂Ω, where λ>0λ>0 and q(p)>pq(p)>p with limp→∞q(p)/p=Q⩾1limp→∞q(p)/p=Q⩾1. We are interested in the characterization of such limits as viscosity solutions of a PDE problem. Both positive and sign-changing solutions are considered.