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Systems of differential equations with fully nonlinear boundary conditions

Published online by Cambridge University Press:  17 April 2009

H.B. Thompson
H.B. Thompson
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072, Australia
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Abstract

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We give sufficient conditions involving f, g and ω in order that systems of differential equations of the form y″ = f(x, y, y′), x in [0, 1] with fully nonlinear boundary conditions of the form g((y(0), y(1)), (y′(0), y′(1))) = 0 have solutions y with (x, y) in . We use Schauder degree theory in a novel space. Well known existence results for the Picard, the periodic and the Neumann boundary conditions follow as special cases of our results.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 197 - 208
Copyright
Copyright © Australian Mathematical Society 1997

References

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