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Upper and lower solution method for nth-order BVPs on an infinite interval

Hairong Lian1*, Junfang Zhao1 and Ravi P Agarwal2

Author Affiliations

1 School of Science, China University of Geosciences, Beijing, 100083, PR China

2 Department of Mathematics, Texas A&M University-Kingsville, Kingsville, Texas, 78363, USA

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Boundary Value Problems 2014, 2014:100  doi:10.1186/1687-2770-2014-100

Published: 7 May 2014


This work is devoted to the study of nth-order ordinary differential equations on a half-line with Sturm-Liouville boundary conditions. The existence results of a solution, and triple solutions, are established by employing a generalized version of the upper and lower solution method, the Schäuder fixed point theorem, and topological degree theory. In our problem the nonlinearity depends on derivatives, and we allow solutions to be unbounded, which is an extra interesting feature.

MSC: 34B15, 34B40.

higher order; boundary value problem; half-line; upper solution; lower solution