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Infinite resonant solutions and turning points in a problem with unbounded bifurcation

By José María Arrieta Algarra, Rosa María Pardo San Gil and Aníbal Rodríguez Bernal

Abstract

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.'

Topics: Ecuaciones diferenciales
Publisher: World Scientific Publishing
Year: 2010
DOI identifier: 10.1142/S021812741002743X
OAI identifier: oai:www.ucm.es:13907
Provided by: EPrints Complutense

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