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  4. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
  5. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.52 (2020), 1st and 2nd Issue
  6. Past and recent contributions to indefinite sublinear elliptic problems
 
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Past and recent contributions to indefinite sublinear elliptic problems

Kaufmann, U.
•
Ramos Quoirin, H.
•
Umezu, K.
2020
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ISSN
0049-4704
DOI
10.13137/2464-8728/30913
http://hdl.handle.net/10077/30913
  • Article

e-ISSN
2464-8728
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.
Journal
Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Subjects
  • elliptic sublinear pr...

  • indefinite

  • strong maximum princi...

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
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Licence
http://creativecommons.org/licenses/by-nc-nd/4.0/
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