Juan Carlos Fernández' Homepage

Research Interests:

• Multiplicity of positive and sign-changing solutions to semilinear elliptic and parabolic equations with critical Sobolev exponent nonlinearities, for instance, Yamabe type problems, Bahri-Coron problem and Yamabe flow.

• Multiplicity of positive and sign-changing solutions to polyharmonic elliptic equations, for example, Q-curvature problems.

• Geometric reductions methods: use of harmonic morphisms, groups of symmetries and isoparametric functions to reduce the dimension of PDE’s.

• Oscillation theory for second and higher even order generalized Emden-Fowler type ODE’s.