Radial solutions of quasilinear equations in Orlicz–Sobolev type spaces

Abstract

This paper is devoted to prove the existence of a nontrivial nonnegative radial solution for the quasilinear elliptic equation−div(φ(|∇u|)∇u)+|u|α−2u=|u|s−2uin RN where N≥2, 1<α≤l⁎m′l′, max⁡{m,α}<s<l⁎, being l,m∈(1,N), l⁎=lNN−l and m′ and l′ the respective conjugate exponents of m and l. The function φ is allowed to belong to a larger class, which includes the special cases appearing in mathematical models in the fields of physics, for instance, nonlinear elasticity, plasticity and generalized Newtonian fluids. The proof is based on variational methods in the Orlicz–Sobolev spaces.