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

We investigate the asymptotic behaviour as p → ∞ of sequences of solutions of the equation { − Δ p u = λ | u | q ( p ) − 2 u in Ω , u = 0 on ∂ Ω , where λ > 0 and q ( p ) > p with lim p → ∞ 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.