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On the First Conjugate Point Function for Nonlinear Differential Equations

Published online by Cambridge University Press:  20 November 2018

Allan C. Peterson and
Dwight V. Sukup
Allan C. Peterson
Affiliation:
University of Nebraska-Lincoln Lincoln, Nebraska 68508
Dwight V. Sukup
Affiliation:
University of South Dakota Vermillion, South Dakota 57069
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Abstract

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We are concerned with the nth order differential equation y(n) = (x, y, y′, …,y(n-1)), where it is assumed throughout that f is continuous on [α,β) × Rn, α < β≤∞, and that solutions of initial value problems are unique and exist on [α, β). The definition of the first conjugate point function η1(t) for linear homogeneous equations is extended to this nonlinear case. Our main concern is what properties of this conjugacy function are valid in the nonlinear case.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 4 , October 1975, pp. 577 - 585
Copyright
Copyright © Canadian Mathematical Society 1975

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