On eigenvalue problems with Robin type boundary conditions having indefinite coefficients
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.
Document Type: Research Article
Affiliations: Faculty of Engineering, Maebashi Institute of Technology, Maebashi 371-0816, Japan
Publication date: November 1, 2006