Measure Data Problems for a Class of Elliptic Equations with Mixed Absorption-Reaction
Marie‐Françoise Bidaut‐Véron, Marta García‐Huidobro, Лаурент Верон · Advanced Nonlinear Studies · 2021
Abstract In the present paper, we study the existence of nonnegative solutions to the Dirichlet problem ℒ p , q M u := - Δ u + u p - M | ∇ u | q = μ {{\mathcal{L}}^{{M}}_{p,q}u:=-\Delta u+u^{p}-M| abla u|^{q}=\mu} in a domain Ω ⊂ ℝ N {\Omega\subset\mathbb{R}^{N}} where μ is a nonnegative Radon measure, when p > 1 {p>1} , q > 1 {q>1} and M ≥ 0 {M\geq 0} . We also give conditions under which nonnegative solutions of ℒ p , q M u = 0 {{\mathcal{L}}^{{M}}_{p,q}u=0} in Ω ∖ K {\Omega\setminus K} , where K is a compact subset of Ω, can be extended as a solution of the same equation in Ω.