Inhomogeneous periodic parabolic problems with indefinite data

GODOY, T.; KAUFMANN, U.

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY

AUSTRALIAN MATHEMATICS PUBL ASSOC INC

Año: 2011 vol. 84 p. 516 - 524

0004-9727

Let Ω⊂R^{N} be a smooth bounded domain and let f≡0 be a possibly discontinuous and unbounded function. We give a necessary and sufficient condition on f for the existence of positive solutions for all λ>0 of Dirichlet periodic parabolic problems of the form Lu=h(x,t,u)+λf(x,t), where h is a nonnegative Carathéodory function that is sublinear at infinity. When this condition is not fulfilled, under some additional assumptions on h we characterize the set of λ′s for which the aforementioned problem possesses some positive solution.