(Università degli Studi dell'Insubria)
Higher order Lane-Emden type systems
Abstract: We
will discuss existence of solutions to Hamiltonian Lane-Emden type
systems where in place of the Laplace operator we take into account the
polyharmonic operator. If the operators have different orders the
problem is non-variational: here we prove existence on a ball by
exploiting continuation method and a priori estimates. Moreover, we can
prove uniqueness in a particular case. When the polyharmonic operators
have the same order then the system turns out to be variational and in
this case we obtain existence on a smooth bounded domain by means of
the Linking Theorem in the context of fractional order Sobolev spaces.
