RT Journal Article
T1 Constant sign solutions of two-point fourth order problems
A1 Cabada Fernández, Alberto
A1 Fernández Gómez, Carlos
K1 Fourth order boundary value problem
K1 Maximum principles
K1 Lower and upper solutions
AB In this paper we characterize the sign of the Green’s function related to the fourth order linear operator u(4) + M u 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. When M > 0 the best estimate follows from spectral theory. When M < 0, we obtain an estimation by studying the disconjugacy properties of the solutions of the homogeneous equation u(4) + M u = 0. The optimal value is attained by studying the exact expression of the Green’s function. Such study allow us to ensure that there is no real parameter M for which the Green’s function is positive on (0, 1) × (0, 1). Moreover, we obtain maximum principles of this operator when the solutions verify suitable non-homogeneous boundary conditions. We apply the obtained results, by means of the method of lower and upper solutions, to nonlinear problems coupled with these boundary conditions.Keywords: Fourth order boundary value problem; Maximum principles; Lower and upper solutions
PB Elsevier
SN 0096-3003
YR 2015
FD 2015-07-15
LK https://hdl.handle.net/10347/45719
UL https://hdl.handle.net/10347/45719
LA eng
NO Alberto Cabada, Carlos Fernández-Gómez, Constant sign solutions of two-point fourth order problems, Applied Mathematics and Computation, Volume 263, 2015, Pages 122-133, ISSN 0096-3003, https://doi.org/10.1016/j.amc.2015.03.112. (https://www.sciencedirect.com/science/article/pii/S0096300315004269)
NO Partially supported by Ministerio de Educación y Ciencia, Spain, project MTM2010- 15314
DS Minerva
RD 24 abr 2026