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Resonance and non-resonance in terms of average values. II

Published online by Cambridge University Press:  12 July 2007

M. N. Nkashama  and
S. B. Robinson
M. N. Nkashama
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294-1170, USA ([email protected])
S. B. Robinson
Affiliation:
Department of Mathematics and Computer Science, Wake Forest University, Winston-Salem, NC 27109, USA ([email protected])
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Abstract

We prove existence results for semilinear elliptic boundary-value problems in both the resonance and non-resonance cases. What sets our results apart is that we impose sufficient conditions for solvability in terms of the (asymptotic) average values of the nonlinearities, thus allowing the nonlinear term to have significant oscillations outside the given spectral gap as long as it remains within the interval on the average in some sense. This work generalizes the results of a previous paper, which dealt exclusively with the ordinary differential equation (ODE) case and relied on ODE techniques.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 5 , October 2001 , pp. 1217 - 1235
Copyright
Copyright © Royal Society of Edinburgh 2001

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