We generalize the Maximum Principle for free end point optimal control problems involving sweeping systems derived in [de Pinho MdR, Ferreira MMA, Smirnov GV. Optimal processes. Set-Valued Var Anal. 2019;27(2):523–548] to cover case where constraints are time dependent and is constrained a set. As 2019;27(2):523–548], an ingenious smooth approximating family of standard differential equations p...

This paper deals with the boundary value problem involving the differential equation begin{equation*}     ell y:=-y''+qy=lambda y,  end{equation*}  subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$  begin{equation*}     y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), end{equation*} where $q(x),  a_1 , a_2$ are  rea...