Constant sign solutions of two-point fourth order problems

Alberto Cabada and Carlos Fernández-Gómez

Applied Mathematics and Computation, 2015, vol. 263, issue C, 122-133

Abstract: In this paper we characterize the sign of the Green’s function related to the fourth order linear operator u(4) + Mu coupled with the two point boundary conditions u(1) = u(0) = u′(0) = u′′(0) = 0. We obtain the exact values on the real parameter M for which the related Green’s function is negative in (0, 1) × (0, 1). Such property is equivalent to the fact that the operator satisfies a maximum principle in the space of functions that fulfil the homogeneous boundary conditions.

Keywords: Fourth order boundary value problem; Maximum principles; Lower and upper solutions (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:263:y:2015:i:c:p:122-133

DOI: 10.1016/j.amc.2015.03.112

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