Arrieta Algarra, José MaríaPardo San Gil, Rosa MaríaRodríguez Bernal, Aníbal2023-06-202023-06-202007-040308-210510.1017/S0308210505000363https://hdl.handle.net/20.500.14352/49721We consider an elliptic equation with a nonlinear boundary condition which is asymptotically linear at infinity and which depends on a parameter. As the parameter crosses some critical values, there appear certain resonances in the equation producing solutions that bifurcate from infinity. We study the bifurcation branches, characterize when they are sub- or supercritical and analyse the stability type of the solutions. Furthermore, we apply these results and techniques to obtain Landesman–Lazer-type conditions guaranteeing the existence of solutions in the resonant case and to obtain an anti-maximum principleengjournal articlehttp://journals.cambridge.org/action/displayJournal?jid=PRMhttp://www.ingentaconnect.com/content/rse/procaopen access517.9Reaction-diffusion equationsParabolic problemsBlow-upAttractorsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias