Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms. (August 2020) - Hara, Takanobu; Seesanea, Adisak
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.