On Variational Multivalued Elliptic Equations on a Bounded Domain in the Presence of Critical Growth

2013/10/22 by J.V. Gonçalves, J. V. Goncalves, Goncalves, J. V. +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1310.5908

18 pages

arxiv created 2013/10/22 · openalex publication_date 2013/10/22 · arxiv updated 2013/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop arguments on the critical point theory for locally Lipschitz functionals on Orlicz-Sobolev spaces, along with convexity and compactness techniques to investigate existence of solution of the multivalued equation - Δ_Φ u ∈ ∂ j(.,u) + λh in Ω, where Ω⊂ \bf R^N is a bounded smooth domain, Φ: \r \longrightarrow [0,∞) is a suitable N-function, Δ_Φ is the corresponding Φ-Laplacian, λ> 0 is a parameter, h:Ω→\r is integrable and ∂ j(., u) is the subdifferential of a function j associated with critical growth.

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