Maximal Solutions of Semilinear Elliptic Equations with Locally Integrable Forcing Term

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We study the existence of a maximal solution of - u+g(u)=f(x) in a domain ⊂ ⁿ with compact boundary, assuming that f∈ (L¹loc())+ and that g is nondecreasing, g(0)≥ 0 and g satisfies the Keller-Osserman condition. We show that if the boundary satisfies the classical C₁,₂ Wiener criterion then the maximal solution is a large solution, i.e., it blows up everywhere on the boundary. In addition we discuss the question of uniqueness of large solutions.