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arXiv · 1610.07872

Positivity results for indefinite sublinear elliptic problems via a continuity argument

Uriel Kaufmann·Humberto Ramos Quoirin·Kenichiro Umezu
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Abstract

We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum principle does not apply to. Our approach is based on a continuity argument combined with variational techniques, the sub and supersolutions method and some a priori bounds. Both Dirichlet and Neumann homogeneous boundary conditions are considered. As a byproduct, we deduce some existence and uniqueness results. Finally, as an application, we derive some positivity results for indefinite concave-convex type problems.

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Uriel Kaufmann, Humberto Ramos Quoirin, Kenichiro Umezu. 2016-10-25. Positivity results for indefinite sublinear elliptic problems via a continuity argument. https://arxiv.org/abs/1610.07872

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