RT Journal Article
T1 Boundary value problems for nonlinear second-order functional differential equations with piecewise constant arguments
A1 Buedo Fernández, Sebastián
A1 Cao Labora, Daniel
A1 Rodríguez López, Rosana
K1 Boundary value problems
K1 Monotone iterative technique
K1 Piecewise constant functional dependence
K1 Second-order functional differential equations
K1 Upper and lower solutions
AB In this paper, we consider a class of nonlinear second-order functional differential equations with piecewise constant arguments with applications to a thermostat that is controlled by the introduction of functional terms in the temperature and the speed of change of the temperature at some fixed instants. We first prove some comparison results for boundary value problems associated to linear delay differential equations that allow to give a priori bounds for the derivative of the solutions, so that we can control not only the values of the solutions but also their rate of change. Then, we develop the method of upper and lower solutions and the monotone iterative technique in order to deduce the existence of solutions in a certain region (and find their approximations) for a class of boundary value problems, which include the periodic case. In the approximation process, since the sequences of the derivatives for the approximate solutions are, in general, not monotonic, we also give some estimates for these derivatives. We complete the paper with some examples and conclusions
PB Wiley
SN 0170-4214
YR 2022
FD 2022
LK http://hdl.handle.net/10347/30763
UL http://hdl.handle.net/10347/30763
LA eng
NO Buedo-Fernández S, Cao Labora D, Rodríguez-López R. Boundary value problems for nonlinear second-order functional differential equations with piecewise constant arguments. Math Meth Appl Sci. 2022;1-35. doi:10.1002/mma.8878
NO Agencia Estatal de Investigación, Grant/Award Number: PID2020-113275GB-I00 and MTM2016-75140-P; Ministerio de Educación, Cultura y Deporte, Grant/Award Number: FPU16/04168 and FPU16/04416; Xunta de Galicia, Grant/Award Number: ED431C 2019/02
DS Minerva
RD 27 abr 2026