An elliptic equation with singular nonlinearity



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Díaz Díaz, Jesús Ildefonso and Morel, J.M. and Oswald, L. (1987) An elliptic equation with singular nonlinearity. Communications in Partial Differential Equations , 12 (12). pp. 1333-1344. ISSN 0360-5302

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The purpose of this paper is to study the problem (P) −Δu+u−α=f in Ω, u=0 on ∂Ω, u−α∈L1(Ω), u>0 in Ω, where Ω is a bounded smooth open set of RN, f≥0, f∈L1(Ω) and 0<α<1. When α≤0 this problem corresponds to a monotone semilinear equation for which the existence and uniqueness of solutions are well known. On the other hand, semilinear equations with nonmonotone perturbations have also been considered in the literature by many different methods. The originality of our study comes from the singularity of the nonlinearity in (P).

Item Type:Article
Uncontrolled Keywords:existence; positive solutions; singular nonlinearity; nonexistence; sub- and supersolutions; monotone iteration scheme; maximal solution; energy functional
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16410
Deposited On:18 Sep 2012 08:53
Last Modified:12 Dec 2018 15:08

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