Europe/Lisbon
Room 6.2.52, Faculty of Sciences, University of Lisbon — Online

Delia Schiera
Delia Schiera, Instituto Superior Técnico, Universidade de Lisboa

On a pure Neumann Lane-Emden system: existence, convergence, and related results

We will consider a Lane-Emden system on a bounded regular domain with Neumann boundary conditions and (sub)critical nonlinearities. In the critical regime, we show that, under suitable conditions on the exponents in the nonlinearities, least-energy (sign-changing) solutions exist. Moreover, through a suitable nonlinear eigenvalue problem, we prove convergence of solutions in dependence of the exponents of the nonlinearities in the (sub)critical range. Finally, I will briefly discuss related results on multiplicity, symmetry breaking, and regularity.

Based on joint works with A. Pistoia, A. Saldaña and H. Tavares.