Bifurcation for a logistic elliptic equation with nonlinear boundary conditions: A limiting case
Bifurcation for a logistic elliptic equation with nonlinear boundary conditions: A limiting case
复制标题
具有非线性边界条件的 Logistic 椭圆方程的分岔：极限情况
DOI：
10.1016/j.jmaa.2015.04.005
复制
发表时间：
2015
影响因子：
1.3
通讯作者：
Humberto Ramos Quoirin and Kenichiro Umezu
中科院分区：
文献类型：
--
作者：
Kaufmann Uriel;Ramos Quoirin Humberto;Umezu Kenichiro;Humberto Ramos Quoirin and Kenichiro Umezu;Humberto Ramos Quoirin and Kenichiro Umezu;Humberto Ramos Quoirin and Kenichiro Umezu;Humberto Ramos Quoirin and Kenichiro Umezu
研究了一类具非线性边界条件的Logistic椭圆型方程的零解分支。由于边界项缺乏正则性，Crandall和Rabinowitz关于简单特征值分支的抽象理论不再适用。利用Whyburn的正则化方法和拓扑方法证明了非平凡非负弱解的子连续统的存在性及其在无穷远处的整体性态。还研究了零点分岔分量的方向。本文讨论了我们以前工作[19]的一个极限情况，其中考虑了变号非线性边界条件的情况。
We investigate bifurcation from the zero solution for a logistic elliptic equation with a sign-definite nonlinear boundary condition. In view of the lack of regularity of the term on the boundary, the abstract theory on bifurcation from simple eigenvalues due to Crandall and Rabinowitz does not apply. A regularization procedure and a topological method due to Whyburn are used to prove the existence and the global behavior at infinity of a subcontinuum of nontrivial non-negative weak solutions. The direction of the bifurcation component at zero is also investigated. This paper treats a limiting case of our previous work [19], where the case of sign-changing nonlinear boundary conditions is considered.