Critical Point Theory

Prof.dr. Vicenţiu Rădulescu

 

1. Ekeland’s variational principle, deformation and pseudogradient lemmas. The Palais-Smale condition.
2. The Mountain Pass theorem of Ambrosetti and Rabinowitz. Regularity of solutions. Examples to subcritical elliptic problems. Non-existence results in the supercritical case.
3. The Saddle Point theorem, the Ghoussoub-Preiss theorem an symmetric critical point theorems. Applications to boundary value problems and to hemivariational inequalities.
4. Nonlinear PDEs in Sobolev spaces with variable exponent and in Orlicz spaces. Existence and multiplicity of solutions.

Bibliography

 

1. H. Brezis and L. Nirenberg, Nonlinear Functional Analysis and Applications to Partial Differential Equations, in preparation.
2. J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer Verlag, 1989.
3. D. Motreanu and V. Radulescu, Variational and Nonvariational Methods in Nonlinear Analysis and Boundary Value Problems, Nonconvex Optimization and Its Applications, Vol. 67, Kluwer Academic Publishers, Dordrecht, 2003.
4. M. Struwe, Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer Verlag, 2000.
5. M. Willem, Minimax Theorems, Progress in Nonlinear Differential Equations and their Applications, Birkhauser Verlag, 1996.