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Oscillation theorems for semilinear elliptic differential operators

Published online by Cambridge University Press:  14 November 2011

Manabu Naito  and
Norio Yoshida
Manabu Naito
Affiliation:
Hiroshima University, Japan
Norio Yoshida
Affiliation:
Iwate University, Morioka, Japan
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Synopsis

The semilinear elliptic differential operator L[u] = Δu + c(x, u) is studied and sufficient conditions are derived for all solutions of uL[u] ≦ 0 with suitable boundary conditions to be oscillatory in unbounded domains of Rn. Here, unbounded domains to be considered are cones, strips and cylinders in Rn. The results are based on the conditions for the non-existence of positive solutions of ordinary differential inequalities.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 135 - 151
Copyright
Copyright © Royal Society of Edinburgh 1978

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