%0 Journal Article
%A Arrieta Algarra, José María
%A Pardo San Gil, Rosa María
%A Rodríguez Bernal, Aníbal
%T Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity
%D 2007
%@ 0308-2105
%U https://hdl.handle.net/20.500.14352/49721
%X We 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 principle
%~