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Boundary-value problems for weakly nonlinear ordinary differential equations

Published online by Cambridge University Press:  17 April 2009

E.N. Dancer
Affiliation:
Department of Mathematics, University of New England, Armidale, New South Wales.
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Abstract

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In this paper, we announce results on the Dirichlet and periodic boundary-value problems for the equation -x″(t) = g(x(t)) – f(t) on [0, π]. We consider degenerate cases not covered by the author's earlier work.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Dancer, E.N., “On a nonlinear elliptic boundary-value problem”, Bull. Austral. Math. Soc. 12 (1975), 399405.CrossRefGoogle Scholar
[2]Dancer, E.N., “On the Dirichlet problem for weakly nonlinear elliptic partial differential equations”, Proc. Roy. Soc. Edinburgh Sect. A (to appear).Google Scholar
[3]Ehrmann, Hans, “Über die Existenz der Lösungen von Randwertaufgaben bei gewöhnlichen nichtlinearen Differentialgleichungen zweiter Ordnung”, Math. Ann. 134 (1957), 167194.CrossRefGoogle Scholar
[4]Fučík, Svatopluk and Lovicar, Vladimír, “Periodic solutions of the equation x″(t) + g(x(t)) = p(t)”, Časopis Pěst. Mat. 100 (1975), 160175.CrossRefGoogle Scholar
[5]Lazer, A.C. and Leach, D.E., “Bounded perturbations of forced harmonic oscillators at resonance”, Ann. Mat. Pura Appl. 82 (1969), 4968.CrossRefGoogle Scholar