Maximal solutions of semilinear elliptic equations with locally integrable forcing term
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We study the existence of a maximal solution of −Δu+g(u)=f(x) in a domain Ω ∈ ℝ N with compact boundary, assuming thatf ∈ (L loc 1 (Ω))+ and thatg is nondecreasing,g(0)≥0 andg satisfies the Keller-Osserman condition. We show that if the boundary satisfies the classicalC 1,2 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.
KeywordsElliptic Equation Minimal Solution Nonlinear Elliptic Equation Maximal Solution Large Solution
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