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Almost periodic solutions of nonlinear parabolic equations

Published online by Cambridge University Press:  17 April 2009

Yisong Yang
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, United States of America
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Abstract

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In this note the recent result of Corduneanu on almost periodicity of L2(G)-bounded solutions of nonlinear parabolic equations is extended to the case when the nonlinear growth rate is beyond the first eigenvalue of the associated elliptic boundary value problem.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Corduneanu, C., ‘Almost periodic solutions to nonlinear elliptic and parabolic equations’, TMA, Nonlinear Anal. 7 (1983), 357363.Google Scholar
[2]Corduneanu, C., ‘Almost periodic solutions to some nonlinear parabolic equations’, in Trends in Theory and Practice of Nonlinear Differential Equations, (ed. Lakshmikantham, V.), pp. 139141. (Marcel Dekker, Inc., New York and Basel).Google Scholar
[3]Dolph, C. L., ‘Nonlinear integral equations of the Hammerstein type’, Trans. Amer. Math. Soc. 66 (1949), 289307.CrossRefGoogle Scholar
[4]Fucik, S., Solvability of Nonlinear Equations and Boundary Value Problems (Reidel, Dordrecht, Boston, London, 1980).Google Scholar
[5]Lazer, A. C. and Leach, D. E., ‘On a nonlinear two point boundary value problem’, J. Math. Anal. Appl. 20 (1969), 2027.CrossRefGoogle Scholar
[6]Vejvoda, O., Partial Differential Equations: Time-Periodic Solutions (Martinus Nijhoff, Boston and London, 1982).CrossRefGoogle Scholar