On the solutions of quasilinear elliptic equations with a polynomial-type reaction term

We study existence and boundedness of solutions for the quasilinear elliptic equation -Δ_mu = λ(1+u)^p in a bounded domain O with homogeneous Dirichlet boundary conditions. The assumptions on both the parameters λ and p are fundamental. Strange critical exponents appear when boundedness of solutions is concerned. In our proofs we use techniques from calculus of variations, from critical-point theory, and from the theory of ordinary differential equations.