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On eigenvalue problems with Robin type boundary conditions having indefinite coefficients

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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.

Keywords: Eigenvalue problem; Indefinite Robin boundary condition; Lower estimate; Population dynamics; Principal eigenvalue; Variational characterization

Document Type: Research Article


Affiliations: Faculty of Engineering, Maebashi Institute of Technology, Maebashi 371-0816, Japan

Publication date: November 1, 2006

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