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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Official URL: http://journals.cambridge.org/action/displayJournal?jid=PRM
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 09:02 |
| Last Modified: | 07 Sep 2011 09:02 |
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