Abstract
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.
Acknowledgements
The author would like to thank the referee for valuable comments and suggestions. This research was partly supported by the Grant-in-Aid for Scientific Research (C) (2), No. 16540165, Japan Society for the Promotion of Science.