Nonlinear boundary value problems for discontinuous delayed differential equations

In this paper nonlinear boundary value problems for discontinuous delayed differential equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower solutions, which may be discontinuous. Our analysis can be applied to those phenomena from physics and control theory which have been successfully described by delayed differential equations with discontinuous functions, such as electric, pneumatic, and hydraulic networks. It is also an important step to precede the design of control signals when finite-time or practical stability control are concerned.