Uniqueness of positive solutions for a class of ODE's with Dirichlet boundary conditions
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Date
2004-11-29
Authors
An, Yulian
Ma, Ruyun
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We study the uniqueness of positive solutions of the boundary-value problem
u'' + α(t)u' + ƒ(t, u) = 0, t ∈ (0, b)
u(0) = 0 = 0, u(b) = 0,
where 0 < b < ∞, α ∈ C1[0, ∞) and ƒ ∈ C1([0, ∞) x [0, ∞), [0, ∞)) satisfy suitable conditions. The proof of our main result is based on the shooting method and the Sturm comparison theorem.
Description
Keywords
Boundary value problems, Positive solutions, Uniqueness, Shooting method, Sturm comparison theorem
Citation
An, Y., & Ma, R. (2004). Uniqueness of positive solutions for a class of ODE's with Dirichlet boundary conditions. <i>Electronic Journal of Differential Equations, 2004</i>(142), pp. 1-9.