Global structure of solutions to boundary-value problems of impulsive differential equations

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.

Description

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. <i>Electronic Journal of Differential Equations, 2016</i>(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.

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