Background. Elements of nonlinear functional analysis and Sobolev spaces
theory. Subharmonic functions, comparison principles.
The Perron method. Applications to nonlinear Dirichlet boundary value
The logistic equation: existence of singular solutions. Qualitative
properties of solutions.
The Lane-Emden-Fowler equation with singular nonlinearity and convection
term. Case of singular potentials. Study of the competition between the terms
involved in the equation. Bifurcation results and qualitative properties of
V. Barbu, Partial Differential Equations and Boundary Value Problems,
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H. Brezis and L. Nirenberg, Nonlinear Functional Analysis and Applications to
Partial Differential Equations, in preparation.
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of
Second Order, Springer Verlag, 1983.
V. Radulescu, Singular phenomena in nonlinear elliptic problems. From blow-up
boundary solutions to equations with singular nonlinearities, in Handbook of
Differential Equations: Stationary Partial Differential Equations, 3 (Michel
Chipot, Pavol Quittner, Editors), 2006, to appear.