Document Type
Article
Department/Program
Mathematics
Journal Title
Journal of Differential Equations
Pub Date
2009
Volume
246
Issue
7
First Page
2788
Abstract
General second order quasilinear elliptic systems with nonlinear boundary conditions on bounded domains are formulated into nonlinear mappings between Sobolev spaces. It is shown that the linearized mapping is a Fredholm operator of index zero. This and the abstract global bifurcation theorem of [Jacobo Pejsachowicz, Patrick J. Rabier, Degree theory for C(1) Fredholm mappings of index 0, J. Anal. Math. 76 (1998) 289-319] allow us to carry out bifurcation analysis directly on these elliptic systems. At the abstract level, we establish a unilateral global bifurcation result that is needed when studying positive solutions. Finally, we supply two examples of cross-diffusion population model and chemotaxis model to demonstrate how the theory can be applied. (C) 2008 Elsevier Inc. All rights reserved.
Recommended Citation
Shi, Junping; Shi, Junping; and Wang, Xuefeng, On global bifurcation for quasilinear elliptic systems on bounded domains (2009). Journal of Differential Equations, 246(7), 2788-2812.
10.1016/j.jde.2008.09.009
DOI
10.1016/j.jde.2008.09.009
