Periodic solutions for higher order differential equations with deviating argument

Pan, Lijun

doi:10.1016/j.jmaa.2008.01.096

Cited by 9 publications

(1 citation statement)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other references relevant to the topic are, for instance, the article by Henríquez and Hernández, 18 which was devoted to the analysis of the approximate controllability of control systems given by second‐order semilinear functional differential equations with infinite delay; the work by Sakthivel et al, 19 which is focused on the study of the exact controllability of certain second‐order nonlinear impulsive control differential systems; the study of Shoukaku, 20 about the oscillatory behavior of certain hyperbolic equations with continuous distributed deviating arguments; or Liu and Huang, 21 where the coincidence degree theory was applied to obtain results on the existence and uniqueness of

T

‐periodic solutions for a class of second‐order neutral functional differential equations. The same approach, coincidence degree theory, was applied in 22 to analyze the existence of periodic solutions for higher‐order differential equations with deviating arguments. In this last case, the dependence on the different derivatives

{x}&amp;amp;#x0005E;{(i)}

is linear.…”

Section: Introductionmentioning

confidence: 99%

Boundary value problems for nonlinear second‐order functional differential equations with piecewise constant arguments

Buedo‐Fernández

Labora

Rodríguez‐López

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

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.

show abstract