Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle.
Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
Blow-up for the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential
We give a sufficient condition under which the solutions of the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential blow up. The method is a modified variational approach, in the spirit of the work by Ibrahim et al. [Anal. PDE 4 (2011), 405-460].
Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential
The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential , is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.
Blow-up solutions of the self-dual Chern–Simons–Higgs vortex equation
Boundary value problems for non-parametric surfaces of prescribed mean curvature