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Maximum principles for a class of semilinear elliptic boundary-value problems

Published online by Cambridge University Press:  17 April 2009

Zhang Hailiang
Zhang Hailiang
Affiliation:
Department of MathematicsShaiuxi UniversityTaiyuan 030006The People's Republic of China
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Abstract

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For years it has remained a problem to find suitable functionals satisfying certain maximum principles for solutions of the equation Δu + f(x, u) = 0. In this paper, maximum principles for certain functionals which are defined on solutions of semilinear elliptic equations subject to mixed or Robin boundary conditions are obtained. The principles derived may be used to deduce bounds on important quantities in physical problems of interest.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 1 , August 1995 , pp. 169 - 175
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Payne, L.E. and Stakgold, I., ‘Nonlinear problems in nuclear reactor analysis’, in Proceedings of the Conference on Nonlinear Problems in Physical Sciences and Biology, Lecture Notes in Math. 322 (Springer-Verlag, Berlin, Heidelberg, New York, 1972), pp. 298–307.Google Scholar
[2]Schaefer, P.W. and Sperb, R.P., ‘Maximum principles and bounds in some inhomogeneous elliptic boundary value problems’, SIAM J. Math. Anal. 8 (1977), 871–878.Google Scholar
[3]Protter, M.H. and Weinberger, H.F., Maximum principles in differential equations (Prentice-Hall, Englewood Cliffs, N.J., 1967).Google Scholar
[4]Sperb, R.P., Maximum principles and their applications (Academic Press, New York, 1981).Google Scholar
[5]Hopf, E., ‘A remark on linear elliptic differential equations of the second order’, Proc. Amer. Math. Soc. 3 (1952), 791–793.Google Scholar