On eigenvalue problems with Robin type boundary conditions having indefinite coefficients
On eigenvalue problems with Robin type boundary conditions having indefinite coefficients
复制标题
DOI：
10.1080/00036810500337860
复制
发表时间：
2006-11
影响因子：
1.1
通讯作者：
K. Umezu
中科院分区：
文献类型：
--
作者：
K. Umezu
讨论了带变号系数的Robin型边界条件。首先，研究了相关的线性椭圆特征值问题，利用变分方法讨论了主特征值的存在性。其次，研究了Logistic型半线性椭圆边值问题的正解的单参数依赖结构，所得结果是利用线性特征值问题的主正特征函数构造适当的上下解的结果.
A Robin type boundary condition with a sign-changing coefficient is treated. First, the associated linear elliptic eigenvalue problem is studied, where the existence of a principal eigenvalue is discussed by the use of a variational approach. Second, the associated semilinear elliptic boundary value problem of logistic type is studied and the one parameter-dependent structure of positive solutions is investigated, where results obtained are due to the construction of suitable super- and subsolutions by using the principal positive eigenfunctions of the linear eigenvalue problem.