Method of Forced Monotonicity for Conjugate type Boundary Value Problems for Ordinary Differential Equations
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Published:1988-03-01
Issue:1
Volume:31
Page:79-84
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ISSN:0008-4395
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Container-title:Canadian Mathematical Bulletin
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language:en
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Short-container-title:Can. math. bull.
Author:
Eloe P. W.,Saintignon P. L.
Abstract
AbstractLet 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.
Publisher
Canadian Mathematical Society
Subject
General Mathematics