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

dc.contributor.authorNiu, Yanmin
dc.contributor.authorYan, Baoqiang
dc.date.accessioned2023-06-14T19:00:01Z
dc.date.available2023-06-14T19:00:01Z
dc.date.issued2016-02-25
dc.description.abstractIn 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent23 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationNiu, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16929
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2016, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectComparison arguments
dc.subjectEigenvalues
dc.subjectGlobal bifurcation theorem
dc.subjectMultiple solutions
dc.subjectAsymptotical behavior of solutions
dc.titleGlobal structure of solutions to boundary-value problems of impulsive differential equations
dc.typeArticle

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