Limits as p→∞p→∞ of pp-Laplacian concave–convex problems

We study the behavior as p→∞p→∞ of the sequel of positive weak solutions of the concave–convex problem equation(P ){−div(|∇u|p−2∇u)=λuq(p)+ur(p)inΩu>0inΩu=0on∂Ω, where Ω⊂RnΩ⊂Rn is a bounded domain, λ>0λ>0 and the exponents q,rq,r satisfy limp→∞q(p)p−1=Q,limp→∞r(p)p−1=R,with0