Second-order differential equations with deviating arguments.
In this paper we present some new existence results for singular positone and semipositone boundary value problems of second order delay differential equations. Throughout our nonlinearity may be singular in its dependent variable.
Nonimprovable sufficient conditions for the solvability and unique solvability of the problem are established, where is a continuous operator satisfying the Carathèodory conditions, is a continuous functional, and .
Using the topological transversality method of Granas we prove an existence result for a system of differential inclusions with retardations of the form y'' ∈ F(t,y,y',Φ(y)). The result is applied to the study of the existence of solutions to an equation of the trajectory of an r-stage rocket with retardations.