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Singular phenomena in nonlinear elliptic problems. From blow-up boundary solutions to equations with singular nonlinearities

Domenii publicaţii > Matematica + Tipuri publicaţii > Capitol de carte

Autori: Vicentiu Radulescu

Editorial: Michel Chipot, North Holland, Handbook of Differential Equations: Stationary Partial Differential Equations, 4, p.483-591, 2007.


In this survey we report on some recent results related to various singular phenomena arising
in the study of some classes of nonlinear elliptic equations.We establish qualitative results
on the existence, nonexistence or the uniqueness of solutions and we focus on the following
types of problems: (i) blow-up boundary solutions of logistic equations; (ii) Lane–Emden–
Fowler equations with singular nonlinearities and subquadratic convection term.We study the
combined effects of various terms involved in these problems: sublinear or superlinear nonlinearities,
singular nonlinear terms, convection nonlinearities, as well as sign-changing potentials.
We also take into account bifurcation nonlinear problems and we establish the precise
rate decay of the solution in some concrete situations. Our approach combines standard techniques
based on the maximum principle with nonstandard arguments, such as the Karamata
regular variation theory.

Cuvinte cheie: Nonlinear elliptic equation, Singularity, Boundary blow-up, Bifurcation, Asymptotic analysis, Maximum principle, Karamata regular variation theory