On the principal eigenvalue of a second order linear elliptic problem with an indefinite weight function

1982 ◽  
Vol 179 (2) ◽  
pp. 237-239 ◽  
Author(s):  
Peter Hess
Author(s):  
M. Faierman

We derive asymptotic formulae for the distribution functions of the real parts of the eigenvalues of an oblique derivative problem involving an indefinite weight function.


Author(s):  
K. Daho ◽  
H. Langer

SynopsisSpectral properties of the singular Sturm-Liouville equation –(p−1y′)′ + qy = λry with an indefinite weight function r are studied in . The main tool is the theory of definitisable operators in spaces with an indefinite scalar product.


Author(s):  
K. Daho ◽  
H. Langer

Everitt has shown [1[, that for α ∊ [0, π/2] the undernoted problem (1.1–2) with an indefinite weight function r can be represented by a selfadjoint operator in a suitable Hilbert space. This result is extended to arbitrary α ∊ [0, π), replacing the Hilbert space in some cases by a Pontrjagin space with index one. The problem is also treated in the Krein space generated by the weight function r.


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