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Upper and lower solutions and semilinear second order elliptic equations with non-linear boundary conditions*

Published online by Cambridge University Press:  14 November 2011

J. Mawhin  and
K. Schmitt
J. Mawhin
Affiliation:
Institut de Mathématique Pure et Appliquee, Université Catholique de Louvain, B–1348 Louvain-la-Neuve, Belgium
K. Schmitt
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, U.S.A.
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Synopsis

A general framework is presented for the proof of the existence of classical solutions of second order elliptic equations which satisfy non-linear boundary conditions. The results obtained contain many of the known theorems for such problems and the approach used unifies the various methods of study based upon upper and lower solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 199 - 207
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Amann, H. and Crandall, M. G.. On some existence theorems for semilinear elliptic equations. Indiana Univ. Math. J. 27 (1978), 779–790.CrossRefGoogle Scholar
2Erbe, L. H.. Nonlinear boundary value problems for second order differential equations. J. Differential Equations 7 (1970), 459–472.CrossRefGoogle Scholar
3Erbe, L. H.. Existence of solutions to boundary value problems for second order differential equations. Nonlinear Anal. 6 (1982), 1155–1162.CrossRefGoogle Scholar
4Inkmann, F.. Existence and multiplicity theorems for semilinear elliptic equations with nonlinear boundary conditions. Indiana Univ. Math. J. 31 (1982), 213–221.CrossRefGoogle Scholar
5Leray, J. and Schauder, J.. Topologie et équations fonctionnelles. Ann. Sci. Ecole Norm. Sup. 51 (1934), 45–78.CrossRefGoogle Scholar
6Mawhin, J.. Topological Degree Methods in Nonlinear Boundary Value Problems (Regional Conference in Math., no 40) (Providence, R. I.: Amer. Math. Soc., 1979).CrossRefGoogle Scholar
7Schmitt, K.. Boundary value problems for quasilinear second order elliptic equations. Nonlinear Anal. 2 (1978), 263–309.CrossRefGoogle Scholar