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Method of Forced Monotonicity for Conjugate type Boundary Value Problems for Ordinary Differential Equations

Published online by Cambridge University Press:  20 November 2018

P. W. Eloe  and
P. L. Saintignon
P. W. Eloe
Affiliation:
Department of Mathematics, University of Dayton Dayton, Ohio45469
P. L. Saintignon
Affiliation:
Department of Mathematics, University of Dayton Dayton, Ohio45469
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Abstract

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Let I = [a, b] ⊆ R and let L be an nth order linear differential operator defined on Cn(I). Let 2 ≦ k ≦ n and let a ≦ x1 < x2 < … < xn = b. A method of forced mono tonicity is used to construct monotone sequences that converge to solutions of the conjugate type boundary value problem (BVP) Ly = f(x, y),y(i-1) = rij where 1 ≦i ≦ mj, 1 ≦ j ≦ k, mj = n, and f : I X R → R is continuous. A comparison theorem is employed and the method requires that the Green's function of an associated BVP satisfies certain sign conditions.

Keywords

34B1034B27
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 79 - 84
Copyright
Copyright © Canadian Mathematical Society 1988

References

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