Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/30913
Title: Past and recent contributions to indefinite sublinear elliptic problems
Authors: Kaufmann, U.
Ramos Quoirin, H.
Umezu, K.
Keywords: elliptic sublinear problemindefinitestrong maximum principle
Issue Date: 2020
Publisher: EUT Edizioni Università di Trieste
Source: U. Kaufmann, H. Ramos Quoirin and K. Umezu, "Past and recent contributions to indefinite sublinear elliptic problems" in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 52 (2020)", EUT Edizioni Università di Trieste, Trieste, 2020
Journal: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Abstract: 
We review the inde nite sublinear elliptic equation Δu =a(x)uq in a smooth bounded domain ΩCRN, with Dirichlet or Neumann homogeneous boundary conditions. Here 0 < q < 1 and a is continuous and changes sign, in which case the strong maximum principle does not apply. As a consequence, the set of nonnegative solutions of these problems has a rich structure, featuring in particular both dead core and/or positive solutions. Overall, we are interested in su_x000E_cient and necessary conditions on a and q for the existence of positive solu-
tions. We describe the main results from the past decades, and combine it with our recent contributions. The proofs are briefly sketched.
Type: Article
URI: http://hdl.handle.net/10077/30913
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/30913
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.52 (2020), 1st and 2nd Issue

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