Inhomogeneous periodic parabolic problems with indefinite data

Authors

  • Tomás Godoy
  • Uriel Kaufmann

Keywords:

Periodic parabolic problems, indefinite, sub and supersolutions, elliptic problems

Abstract

Let Ω⊂R^{N} be a smooth bounded domain and let f not identically zero 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. All results remain true for the corresponding elliptic problems. doi:10.1017/S0004972711002553

Published

2011-10-27

Issue

Vol. 84 No. 3 (2011)

Section

Articles
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