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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 ∈ ℝN with compact boundary, assuming thatf ∈ (L 1 loc (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.

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Correspondence to Moshe Marcus.

Additional information

This research was partially supported by an EC Grant through the RTN Program “Front-Singularities”, HPRN-CT-2002-00274.

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Marcus, M., Véron, L. Maximal solutions of semilinear elliptic equations with locally integrable forcing term. Isr. J. Math. 152, 333–348 (2006).

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