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.

报告人简介：

Delia Schiera is a researcher at Instituto Superior Técnico, University of Lisbon, and a member of CAMGSD. She received her Ph.D. in Mathematics from the Università degli Studi dell’Insubria in 2019. Her research focuses on nonlinear partial differential equations and nonlinear analysis, with particular interests in elliptic equations and systems, Lane–Emden type problems, symmetry, spectral problems, and variational methods.