On global bifurcation for quasilinear elliptic systems on bounded domains
On global bifurcation for quasilinear elliptic systems on bounded domains
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有界域上拟线性椭圆系统的全局分岔
DOI：
10.1016/j.jde.2008.09.009
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发表时间：
2009-04-01
影响因子：
2.4
通讯作者：
Wang, Xuefeng
中科院分区：
文献类型：
--
作者：
Shi, Junping;Wang, Xuefeng
有界域上具有非线性边界条件的一般二阶拟线性椭圆系统被公式化为 Sobolev 空间之间的非线性映射。结果表明，线性化映射是索引为零的 Fredholm 算子。这和[Jacobo Pejsachowicz、Patrick J. Rabier、索引 0 的 C(1) Fredholm 映射的度数理论、J. Anal 的抽象全局分岔定理。数学。 76 (1998) 289-319]允许我们直接在这些椭圆系统上进行分岔分析。在抽象层面上，我们建立了研究正解时所需的单边全局分岔结果。最后，我们提供了交叉扩散群体模型和趋化性模型的两个例子来演示如何应用该理论。 (C) 2008 Elsevier Inc. 保留所有权利。
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.