Niu, YanminYan, Baoqiang2023-06-142023-06-142016-02-25Niu, Y., & Yan, B. (2016). Global structure of solutions to boundary-value problems of impulsive differential equations. Electronic Journal of Differential Equations, 2016(55), pp. 1-23.1072-6691https://hdl.handle.net/10877/16929In 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.Text23 pages1 file (.pdf)enAttribution 4.0 InternationalComparison argumentsEigenvaluesGlobal bifurcation theoremMultiple solutionsAsymptotical behavior of solutionsArticle