Liu, YujiGe, Weigao2021-01-082021-01-082003-09-04Liu, Y., & Ge, W. (2003). Positive solutions of boundary-value problems for 2m-order differential equations. <i>Electronic Journal of Differential Equations, 2003</i>(89), pp. 1-12.1072-6691https://hdl.handle.net/10877/13097This article concerns the existence of positive solutions to the differential equation (-1)m x(2m)(t) = ƒ(t, x(t), x'(t),...,x(m)(t)), 0 < t < π, subject to boundary condition x(2i)(0) = x(2i) (π) = 0, or to the boundary condition x(2i)(0) = x(2i + 1) (π) = 0, for i = 0,1,...,m - 1. Sufficient conditions for the existence of at least one positive solution of each boundary-value problem are established. Motivated by references [7, 17, 21], the emphasis in this paper is that f depends on all higher-order derivatives.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalHigher-order differential equationBoundary-value problemPositive solutionsFixed point theoremArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.