Existence of solutions for functional antiperiodic boundary value problems (Q2770655)

The author discusses antiperiodic boundary value problems for functional-differential equations of the type NEWLINE\[NEWLINEx'(t)=f(t,x_t), \;t\in [0.T], \;x(s)=x(0)=-x(T)\;\text{for} s\in [-\tau,0](\text{with a given} \tau >0)\tag{1} NEWLINE\]NEWLINE where \(x_t(s)=x(t+s)\) for \(s\in [-\tau,0]\). NEWLINENEWLINENEWLINEAssuming suitable conditions the author proves theorems on the existence and uniqueness of solutions to such problems and on approximations of solutions by monotone sequences of succesive approximations. The lower and upper solutions method is applied.