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

Arrieta Algarra, José María and Pardo San Gil, Rosa María and Rodríguez Bernal, Aníbal (2010) Infinite resonant solutions and turning points in a problem with unbounded bifurcation. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 20 (9). 2885-2896 . ISSN 0218-1274

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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.''

Item Type:Article
Uncontrolled Keywords:Bifurcation from infinity; Nonlinear boundary conditions; Steklov eigenvalues; Turning points; Resonant solutions
Subjects:Sciences > Mathematics > Differential equations
ID Code:13907
Deposited On:17 Nov 2011 08:14
Last Modified:06 Feb 2014 09:55

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