Existence of least energy nodal solution with two nodal domains for a generalized Kirchhoff problem in an Orlicz Sobolev space

الأصل · EN

We show the existence of a nodal solution with two nodal domains for a generalized Kirchhoff equation of the type -M(∫ΩΦ(|∇ u|)dx)ΔΦu = f(u) in Ω, u=0 on ∂Ω, where Ω is a bounded domain in Rⁿ, M is a general C¹ class function, f is a superlinear C¹ class function with subcritical growth, Φ is defined for t∈ R by setting Φ(t)=∫₀|ᵗ|ϕ(s)sds, ΔΦ is the operator ΔΦu:=div(ϕ(|∇ u|)∇ u). The proof is based on a minimization argument and a quantitative deformation lemma.