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Singular phenomena in nonlinear elliptic problems: from blow-up boundary solutions to equations with singular nonlinearities. (English) Zbl 1193.35053
Chipot, Michel (ed.), Handbook of differential equations: Stationary partial differential equations. Vol. IV. Amsterdam: Elsevier/North Holland (ISBN 978-0-444-53036-3/hbk). Handbook of Differential Equations, 485-593 (2007).
The author reports on some recent result related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. In this survey, the author dissertates some qualitative results on the existence, nonexistence or uniqueness of solutions.
Reviewer: Jiaqi Mo (Wuhu)
MSC:
35J60Nonlinear elliptic equations
35-02Research monographs (partial differential equations)
35J20Second order elliptic equations, variational methods
35A01Existence problems for PDE: global existence, local existence, non-existence
35A02Uniqueness problems for PDE: global uniqueness, local uniqueness, non-uniqueness