Monotone Methods in PDEs

Prof.dr. Vicenţiu Rădulescu

 

1. Background. Elements of nonlinear functional analysis and Sobolev spaces theory. Subharmonic functions, comparison principles.
2. The Perron method. Applications to nonlinear Dirichlet boundary value problems.
3. The logistic equation: existence of singular solutions. Qualitative properties of solutions.
4. 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 solutions.

Bibliography

 

1. V. Barbu, Partial Differential Equations and Boundary Value Problems, Mathematics and its Applications, vol. 441, Kluwer, 1998.
2. H. Brezis and L. Nirenberg, Nonlinear Functional Analysis and Applications to Partial Differential Equations, in preparation.
3. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer Verlag, 1983.
4. 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.