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Minimal and maximal solutions for two-point boundary-value problems. (English) Zbl 1028.34015
The authors apply the monotone iterative method to the nonlinear implicit second-order boundary value problem \(f(t,x,x',x'')=0\), \(0\leq a \leq t \leq b\), \(x(a)=A\), \(x'(b)=B\), to obtain minimal and maximal solutions. They assume regularity properties on the function \(f\) and their derivatives on suitable sets of \([a,b] \times \mathbb{R}^3\). The proof is based on the hypothesis of the existence of barrier strips related to the function \(f\).
MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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