On eigenvalue problems with Robin type boundary conditions having indefinite coefficients |
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Authors: | Kenichiro Umezu |
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Affiliation: | 1. Faculty of Engineering , Maebashi Institute of Technology , Maebashi 371-0816, Japan ken@maebashi-it.ac.jp |
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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. |
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Keywords: | Eigenvalue problem Indefinite Robin boundary condition Principal eigenvalue Variational characterization Lower estimate Population dynamics |
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