Positive solutions of boundary-value problems for 2m-order differential equations

Date

2003-09-04

Authors

Liu, Yuji
Ge, Weigao

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

This 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.

Description

Keywords

Higher-order differential equation, Boundary-value problem, Positive solutions, Fixed point theorem

Citation

Liu, 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.

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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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