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An Existence Theorem for Nonlinear Boundary Value Problems

Published online by Cambridge University Press:  20 November 2018

W. L. McCandless
W. L. McCandless*
Affiliation:
Department of Mathematics, Mount Allison University, Sackville, New Brunswick
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Boundary value problems for ordinary differential equations have long been the subject of extensive research activity. In particular, questions concerning the existence and uniqueness of solutions for these problems have received much attention, and algebraic fixed-point theorems have served as important tools in such investigations. For example Picard [8] based his pioneering work in this area on the use of successive approximation techniques, and recently his classical methods have been refined and extended to more general nonlinear problems (see [1] and [4]). The standard procedure for applying these techniques requires that the boundary value problem under consideration first be converted into an equivalent integral equation through the choice of a suitable Green’s function. The resulting theory is consequently limited to problems for which such a formulation is possible.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 5 , February 1975 , pp. 693 - 701
Copyright
Copyright © Canadian Mathematical Society 1975

References

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