Global structure of solutions to boundary-value problems of impulsive differential equations
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Date
2016-02-25
Authors
Niu, Yanmin
Yan, Baoqiang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the structure of global solutions to the boundary-value problem
-x″(t) + ƒ(t, x) = λαx(t), t ∈ (0, 1), t ≠ 1/2,
∆x|t=1/2 = β1x(1/2), ∆x′|t=1/2 = -β2x(1/2),
x(0) = x(1) = 0,
where λ ≠ 0, β1 ≥ β2 ≥ 0, ∆x|t=1/2 = x(1/2 + 0) - x(1/2), ∆x′|t=1/2 = x′(1/2 + 0) - x′(1/2 - 0), and ƒ : [0, 1] x ℝ → ℝ, α : [0, 1] → (0, +∞) are continuous. By a comparison principle and spectral properties of the corresponding linear equations, we prove the existence of solutions by using Rabinowitz-type global bifurcation theorems, and obtain results on the behavior of positive solutions for large λ where ƒ(x) = xp+1.
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Keywords
Comparison arguments, Eigenvalues, Global bifurcation theorem, Multiple solutions, Asymptotical behavior of solutions
Citation
Niu, Y., & Yan, B. (2016). Global structure of solutions to boundary-value problems of impulsive differential equations. Electronic Journal of Differential Equations, 2016(55), pp. 1-23.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.