Let Ω ⊂ RN be a smooth bounded domain. We give sufficient conditions (which are also necessary in many cases) on two nonnegative functions a, b that are possibly discontinuous and unbounded for the existence of nonnegative solutions for semilinear Dirichlet periodic parabolic problems of the form Lu = λa (x, t) up - b (x, t) uq in Ω × R, where 0 < p, q < 1 and λ > 0. In some cases we also show the existence of solutions uλ in the interior of the positive cone and that uλ can be chosen such that λ → uλ is differentiable and increasing. A uniqueness theorem is also given in the case p ≤ q. All results remain valid for the corresponding elliptic problems.
@article{urn:eudml:doc:41886,
title = {Periodic parabolic problems with nonlinearities indefinite in sign.},
journal = {Publicacions Matem\`atiques},
year = {2007},
pages = {45-57},
mrnumber = {MR2307146},
zbl = {1146.35051},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41886}
}
Godoy, Tomás; Kaufmann, Uriel. Periodic parabolic problems with nonlinearities indefinite in sign.. Publicacions Matemàtiques, (2007), pp. 45-57. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41886/