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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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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.
tions. We describe the main results from the past decades, and combine it with our recent contributions. The proofs are briefly sketched.
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
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