The sub-supersolution method for weak solutions

Montenegro, Marcelo;Ponce, Augusto
(2008) Proceedings of the American Mathematical Society — Vol. 136, n° 7, p. 2429-2438 (2008)

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Abstract
We extend the method of sub and supersolutions in order to prove existence of L-1-solutions of the equation -Delta u = f(x, u) in Omega, where f is a Caratheodory function. The proof is based on Schauder's fixed point theorem.
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Montenegro, M., & Ponce, A. (2008). The sub-supersolution method for weak solutions. Proceedings of the American Mathematical Society, 136(7), 2429-2438. https://doi.org/10.1090/S0002-9939-08-09231-9 (Original work published 2008)