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Global Positive Solutions of Semilinear Elliptic Equations

Published online by Cambridge University Press:  20 November 2018

Ezzat S. Noussair  and
Charles A. Swanson
Ezzat S. Noussair
Affiliation:
University of New South Wales, Kensington, Australia
Charles A. Swanson
Affiliation:
University of British Columbia, Vancouver, British Columbia
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The semilinear elliptic boundary value problem

1.1

will be considered in an exterior domain Ω ⊂ Rn, n ≥ 2, with boundary ∂Ω ∊ C2 + α, 0 < α < 1, where

1.2

Di = ∂/∂xi, i = 1, …, n. The coefficients aij, bi in (1.2) are assumed to be real-valued functions defined in Ω ∪ ∂Ω such that each , , and (aij(x)) is uniformly positive definite in every bounded domain in Ω. The Hölder exponent α is understood to be fixed throughout, 0 < α < 1 . The regularity hypotheses on f and g are stated as H 1 near the beginning of Section 2.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 5 , 01 October 1983 , pp. 839 - 861
Copyright
Copyright © Canadian Mathematical Society 1983

References

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