The main goal of this work is to prove Strauss-and Lions-type results for Orlicz-Sobolev spaces. After, we use these results to study the existence of solutions for a class of quasilinear problems in R N .2000 AMS Subject Classification: 35A15, 35J62, 46E30.

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We show the existence of a nodal solution with two nodal domains for a generalized Kirchhoff equation of the typewhere Ω is a bounded domain in R N , M is a general C 1 class function, f is a superlinear C 1 class function with subcritical growth, Φ is defined for t ∈ R by setting Φ(t) = |t| 0 φ(s)sds, ∆Φ is the operator ∆Φu := div(φ(|∇u|)∇u). The proof is based on a minimization argument and a quantitative deformation lemma.

This paper is principally devoted to revisit the remarkable works of Keller and Osserman and generalize some previous results related to the those for the class of quasilinear elliptic problem { div ϕfalse(false|∇ufalse|false)∇u=afalse(xfalse)ffalse(ufalse)inΩ,u≥0inΩ,u=∞on∂Ω,where either Ω⊂boldRN with N≥1 is a smooth bounded domain or Ω=boldRN. The function ϕ includes special cases appearing in mathematical models in nonlinear elasticity, plasticity, generalized Newtonian fluids, and in quantum physics. The proofs are based on comparison principle, variational methods and topological arguments on the Orlicz–Sobolev spaces.

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