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Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity

Arrieta Algarra, José María and Pardo San Gil, Rosa and Rodríguez Bernal, Aníbal (2007) Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 137 (2). pp. 225-252. ISSN 0308-2105

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Abstract

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

Item Type:Article
Uncontrolled Keywords:Reaction-diffusion equations; Parabolic problems; Blow-up; Attractors
Subjects:Sciences > Mathematics > Differential equations
ID Code:13211
Deposited On:07 Sep 2011 07:02
Last Modified:06 Feb 2014 09:43

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