Suggested Topics:
The critical case p=2*
Symmetric solution in symmetric domains
Multiplicity results in semilinear elliptic problems
Regularity theorems for elliptic equations
Linking theorems
Construction of solutions to elliptic problems via bifurcation arguments
Morse theory applied to the multiplicity of solutions to elliptic equations
General stability results for Hamiltonian dynamical systems
Long-time behavior and scattering for the (NLS)
Properties of blowup solutions to the (NLS) in the L^2-critical case
Local existence for the (NLS) in nonstandard spaces
Local existence for the Korteweg-de Vries equation
Local existence for the modified Korteweg-de Vries equation
Self-similar solutions for the cubic (NLS) and vortex filaments
Dispersive equations in periodic domains
Nonlinear smoothing for dispersive equations
Global existence for dispersive equations below energy regulartiy
Further results on scattering for the (NLS)
The damped (NLS) equation: global existence and blow-up
Inverse scattering techniques
The (NLS) on an outer domain
Systems of (NLS) equations: local and global existence, blow-up, ground-states, stability
The inhomogeneous Schrödinger equation
The (NLS) on the half-space
The (NLS) on metric graphs
Dispersive equations with random initial data
The (NLS) with Debye time-delay: global existence and blow-up
The nonlinear heat equation: local and global existence, blow-up
The nonlinear Klein-Gordon equation: local and global existence, blow-up