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A monotone iterative method for boundary value problems of parametric differential equations. (English) Zbl 1013.34005
Consider the initial value problem for the DAE-system ($$\ast$$) $$dx/dy = f(t,x,\lambda)$$, $$0 = g(x,\lambda)$$, $$x(0) = x_0$$, for $$0 \leq t \leq T$$, $$x, \lambda \in \mathbb{R}$$. The authors derive conditions on f and g such that there exist monotone sequences of lower and upper solutions to ($$\ast$$) $$\overline{x}_n$$, $${\overline{\lambda}}_n$$, $${\underline{x}}_n$$, $${\underline{\lambda}}_n$$, $${\underline{x}}_n \leq {\underline{x}}_{n+1} \leq\dots\leq \overline{x}_{n+1} \leq \overline{x}_n$$ converging to minimal and maximal solutions to ($$\ast$$).

##### MSC:
 34A09 Implicit ordinary differential equations, differential-algebraic equations 34A45 Theoretical approximation of solutions to ordinary differential equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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