Critical Point Theory
Prof.dr.
Vicenţiu Rădulescu

Ekeland’s variational principle, deformation and pseudogradient lemmas. The
PalaisSmale condition.

The Mountain Pass theorem of Ambrosetti and Rabinowitz. Regularity of
solutions. Examples to subcritical elliptic problems. Nonexistence results in
the supercritical case.

The Saddle Point theorem, the GhoussoubPreiss theorem an symmetric critical
point theorems. Applications to boundary value problems and to hemivariational
inequalities.

Nonlinear PDEs in Sobolev spaces with variable exponent and in Orlicz spaces.
Existence and multiplicity of solutions.
Bibliography

H. Brezis and L. Nirenberg, Nonlinear Functional Analysis and Applications to
Partial Differential Equations, in preparation.

J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems,
Springer Verlag, 1989.

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.

M. Struwe, Variational Methods. Applications to Nonlinear Partial
Differential Equations and Hamiltonian Systems, Springer Verlag, 2000.

M. Willem, Minimax Theorems, Progress in Nonlinear Differential Equations and
their Applications, Birkhauser Verlag, 1996.