Orlicz-Sobolev versus Holder local minimizer and multiplicity results for quasilinear elliptic equations

2011/09/26 by Fei Fang, Zhong, Tan, Fei, Fang
Arts and Humanities · Mathematics · #35J20 #35J65 #35J70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Historical and Contemporary Political Dynamics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1109.5614

openalex publication_date 2011/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the following boundary value problem (P) -div(a(|∇ u|)∇ u)=f(x,u), & in Ω, u=0, & on ∂Ω with nonhomogeneous principal part. By assuming the nonlinearity f(x, t) being subcritical growth, some abstract results of problem (P) are obtained: (1) Regularity; (2) Orlicz-Sobolev versus Hölder local minimizer; (3) Strong comparison principle. Applying these abstract results and critical point theory, we prove the existence of multiple solutions of problem (P) in an Orlicz-Sobolev space.

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