On global bifurcation for quasilinear elliptic systems on bounded domains |
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Authors: | Junping Shi Xuefeng Wang |
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Institution: | a Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA b School of Mathematics, Harbin Normal University, Harbin, Heilongjiang 150080, PR China c Department of Mathematics, Tulane University, New Orleans, LA 70118, USA |
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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 C1 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. |
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Keywords: | primary 35J55 35B32 secondary 46T20 58C25 92D25 |
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