Maximum and minimum solutions for nonlinear parabolic problems with discontinuitiesMaximum and minimum solutions for nonlinear parabolic problems with discontinuities Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-291998enIn this paper we examine nonlinear parabolic problems with a discontinuous right hand side. Assuming the existence of an upper solution φ and a lower solution ψ such that ψ ≤ φ, we establish the existence of a maximum and a minimum solution in the order interval [ψ, φ]. Our approach does not consider the multivalued interpretation of the problem, but a weak one side “Lipschitz” condition on the discontinuous term. By employing a fixed point theorem for nondecreasing maps, we prove the existence of extremal solutions in [ψ, φ for the original single valued version of the problem.Δημοσίευση σε επιστημονικό περιοδικό http://creativecommons.org/licenses/by/4.0/Proceedings Mathematical Sciences2108 179-187 Kandylakis Dimitrios Κανδυλακης Δημητριος Papageorgiou Nikolaos S. Indian Academy of Sciences Upper solution lower solution evolution triple compact embedding integration by parts Sobolev space regular cone