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

2015/11/16 by Giovany M. Figueiredo, Figueiredo, Giovany M., Jefferson A. Santos +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1511.04980

openalex publication_date 2015/11/16 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We show the existence of a nodal solution with two nodal domains for a\ngeneralized Kirchhoff equation of the type -M
left(
displaystyle
int_
Omega\n
Phi(|
nabla u|)dx
right)
Delta_
Phi u = f(u)


mboxin


Omega,

u=0\n


mboxon


partial
Omega, where \Ω is a bounded domain in\n\R^N, M is a general C¹ class function, f is a superlinear\nC¹ class function with subcritical growth, \Φ is defined for t\∈\n\R by setting \Φ(t)=\∫₀^|t|\φ(s)sds, \Δ_\Φ is the\noperator \Δ_\Φ u:=div(\φ(|\∇ u|)\∇ u). The proof is based on\na minimization argument and a quantitative deformation lemma.\n

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