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