2026-06-07T15:52:05Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/1247302025-10-09T23:48:06Zcom_20.500.14352_14col_20.500.14352_15

On bifurcation from infinity: a compactification approach Arrieta Algarra, José María Fernandes, Juliana Lappicy, Phillipo Acuerdos Transformativos CRUE 2025 We consider a scalar parabolic partial differential equation on the interval with nonlinear boundary conditions that are asymptotically sublinear. As the parameter crosses critical values (e.g. the Steklov eigenvalues), it is known that there are large equilibria that arise through a bifurcation from infinity (i.e., such equilibria converge, after rescaling, to the Steklov eigenfunctions). We provide a compactification approach to the study of such unbounded bifurcation curves of equilibria, their stability, and heteroclinic orbits. In particular, we construct an induced semiflow at infinity such that the Steklov eigenfunctions are equilibria. Moreover, we prove the existence of infinite-time blow-up solutions that converge, after rescaling, to certain eigenfunctions that are equilibria of the induced semiflow at infinity. 2025-10-09T11:34:32Z 2025-10-09T11:34:32Z 2025 journal article Arrieta, J. M., Fernandes, J., & Lappicy, P. On bifurcation from infinity: a compactification approach. Calculus of Variations and Partial Differential Equations. 2025; 64(3): 1-18. 0944-2669 1432-0835 10.1007/s00526-025-02945-3 https://hdl.handle.net/20.500.14352/124730 eng http://creativecommons.org/licenses/by/4.0/ open access Attribution 4.0 International Springer Nature Link