Abstract
AbstractLet Ω⊂ℝNbe a smooth bounded domain and letf⁄≡0 be a possibly discontinuous and unbounded function. We give a necessary and sufficient condition onffor the existence of positive solutions for allλ>0 of Dirichlet periodic parabolic problems of the formLu=h(x,t,u)+λf(x,t), wherehis a nonnegative Carathéodory function that is sublinear at infinity. When this condition is not fulfilled, under some additional assumptions onhwe characterize the set ofλs for which the aforementioned problem possesses some positive solution. All results remain true for the corresponding elliptic problems.
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