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Boundary value problems for ordinary differential equations with deviated arguments. (English) Zbl 1140.34027

Consider the boundary value problem

x ' (t)=f(t,x(t),x(α(t)),x(t),x(β(t)),t[0,T],0=g(x(0),x(T)),(*)

where f, g, α, β are continuous functions. The authors give sufficient conditions such that

(i) (*) has quasisolutions;

(ii) (*) has a unique solution.

The proofs are based on the monotone iterative method. They present two examples satisfying the required assumptions.

34K10Boundary value problems for functional-differential equations
34K07Theoretical approximation of solutions of functional-differential equations
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