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Monotone techniques and semilinear elliptic boundary value problems*

Published online by Cambridge University Press:  14 November 2011

K. J. Brown  and
S. S. Lin
K. J. Brown
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh
S. S. Lin
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh
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Synopsis

This paper considers semilinear elliptic boundary value problems of the form

where the partial derivative ∂f/∂u is bounded above by the least eigenvalue of the linear elliptic operator L. Existence and uniqueness of solutions is proved by using monotone operator theory and sub and supersolution techniques.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 80 , Issue 1-2 , 1978 , pp. 139 - 149
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Amann, H.Existence and multiplicity theorems for semilinear elliptic boundary value problems. Math. Z, 150 (1976), 281–295.CrossRefGoogle Scholar
2Dunninger, D. R. and Locker, J.Monotone operators and nonlinear biharmonic boundary value problems. Pacific J. Math. 60 (1975), 39–48.CrossRefGoogle Scholar
3Ford, W. T.On the first boundary value problem for [h(x, x′, t)]′ = f(x, x′, t). Proc. Amer. Math. Soc. 35 (1972), 491–497.Google Scholar
4Friedman, A.Partial differential equations (New York: Holt, 1969).Google Scholar
5Kato, T.Perturbation theory for linear operators (Berlin: Springer, 1966).Google Scholar
6Kazdan, J. L. Existence and nonexistence for semilinear elliptic equations. In Global analysis and applications II (Vienna: Internat. Atomic Energy Agency, 1974).Google Scholar
7Stuart, C. A.Some bifurcation theory for k-set contractions. Proc. London Math. Soc. 27 (1973), 531–550.CrossRefGoogle Scholar
8Tippett, J.An existence-uniqueness theorem for two point boundary value problems. Siam J. Math. Anal. 5 (1974), 153–157.CrossRefGoogle Scholar
9Vainberg, M. M.Variational method and method of monotone operators (New York: Wiley, 1973).Google Scholar