Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms. (August 2020)

• Record Type: Journal Article
• Authors: Hara, Takanobu; Seesanea, Adisak
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: 35J92 -- 35J20 -- 42B37; Quasilinear elliptic equation -- Measure data -- p-Laplacian -- Wolff potential; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111847
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the existence of positive solutions to quasilinear elliptic equations of the type − Δ p u = σ u q + μ in R n, in the sub-natural growth case 0 < q < p − 1, where Δ p u = ∇ ⋅ ( | ∇ u | p − 2 ∇ u ) is the p -Laplacian with 1 < p < n, and σ and μ are nonnegative Radon measures on R n . We construct minimal generalized solutions under certain generalized energy conditions on σ and μ . To prove this, we give new estimates for interaction between measures. We also construct solutions to equations with several sub-natural growth terms using the same methods.