On a class of similarity solutions of the porous media equation,III |
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Authors: | B.H Gilding |
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Affiliation: | Mathematisch Instituut, Rijksuniversiteit te Leiden, Leiden, The Netherlands |
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Abstract: | It is shown how existence questions for general multiparameter eigenvalue problems can be treated quite simply using degree theory. The equations to be solved are Wn(λ)xn = 0 ≠ xn, n = 1, 2,…, k, where λ ? k and each Wn(λ) is a self-adjoint linear operator on a Hilbert space Hn. The Wn, which may be unbounded, depend continuously on λ in a suitable sense. A coercivity condition for large ∥ λ ∥ is used, and is shown to be equivalent, in the “linear” case, to a standard determinantal definiteness condition. |
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