In this paper a new version of Krasnoselskii’s fixed point theorem in cones, together with a global weak Harnack inequality for nonnegative superharmonic functions are used to investigate the existence of positive solutions of the Dirichlet problem for semi-linear elliptic equations.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
positive solution; fixed point theorem in cones; elliptic boundary value problem; weak Harnack inequality.
R. Precup, Positive solutions of semi-linear elliptic problems via Krasnoselskii type theorems in cones and Harnack’s inequality, in “Mathematical Analysis ans Applications”, eds. V. Radulescu and C. Niculescu, Amer. Inst. Physics, AIP Conference Proceedings, vol. 835, 2006, 125-132. https://doi.org/10.1063/1.2205042
Mathematical Analysis and Applications
American Inst. of Physics
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