Uniqueness of entire solutions to quasilinear equations of p-Laplace type

2022/08/28 by Nguyen Cong Phuc, Phuc, Nguyen Cong, Igor E. Verbitsky +1 · 1 citation
Mathematics · #31B15 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Meromorphic and Entire Functions #Primary 35J92 #Secondary 42B37

paper · pdf · doi:10.48550/arxiv.2208.13272

openalex publication_date 2022/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the uniqueness property for a class of entire solutions to the equation \ -\rm div A(x,∇ u) = σ, u≥ 0 in ℝⁿ,
\liminf_{|x|→ ∞} u = 0, . where σ is a nonnegative locally finite measure in ℝⁿ, absolutely continuous with respect to the p-capacity, and \rm div A(x,∇ u) is the A-Laplace operator, under standard growth and monotonicity assumptions of order p (1

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