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Advanced differential equations with nonlinear boundary conditions. (English) Zbl 1092.34032

Consider the nonlinear boundary value problem

x ' (t)=f(t,c(t),x(α(t))),0=g(x(0),x(T))(*)

under the assumption that f,α and g are continuous functions with bα(t)T. By means of the method of monotone iteration based on lower and upper solutions for (*), the author derives sufficient conditions for (*) to have an extremal solution or a unique solution. Linear advanced differential inequalities are discussed, too.

MSC:
34K10Boundary value problems for functional-differential equations
34A45Theoretical approximation of solutions of ODE