2026-06-29T16:55:33Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/420002023-08-28T00:39:26Zcom_20.500.14352_14col_20.500.14352_15

Infinite resonant solutions and turning points in a problem with unbounded bifurcation Arrieta Algarra, José María Pardo San Gil, Rosa María Rodríguez Bernal, Aníbal 517.9 Bifurcation from infinity Nonlinear boundary conditions Steklov eigenvalues Turning points Resonant solutions Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias Summary: "We consider an elliptic equation −Δu+u=0 with nonlinear boundary conditions ∂u/∂n=λu+g(λ,x,u) , where (g(λ,x,s))/s→0 as |s|→∞ . In [Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 2, 225--252; MR2360769 (2009d:35194); J. Differential Equations 246 (2009), no. 5, 2055--2080; MR2494699 (2010c:35016)] the authors proved the existence of unbounded branches of solutions near a Steklov eigenvalue of odd multiplicity and, among other things, provided tools to decide whether the branch is subcritical or supercritical. In this work, we give conditions on the nonlinearity, guaranteeing the existence of a bifurcating branch which is neither subcritical nor supercritical, having an infinite number of turning points and an infinite number of resonant solutions.'' MEC Grupo 920894 (Comunidad de Madrid - UCM, Spain) MICINN SIMUMAT Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T00:06:49Z 2023-06-20T00:06:49Z 2010 journal article https://hdl.handle.net/20.500.14352/42000 0218-1274 10.1142/S021812741002743X eng MTM2006–08262 GR74/07 PHB2006-003PC open access application/pdf World Scientific Publishing